SD9700010

INIS-SD--004

(n,p) AND (n,a) REACTIONS CROSS-SECTIONSMEASUREMENTS AND SYSTEMATICS AROUND

14 MEV NEUTRON ENERGY

By

IBRAHIM A/ RAHIM SHADDAD

A thesis submitted in fulfilment of the requirementsfor the degree of Doctor of Philosophy

> Physics DepartmentFaculty of Science

University of Khartoum

Khartoum, 1995

[POOR QUALITY' ORIGINAL '

Dedicated to

My parentsMy wife OmymaMy children Niema andAbubaker

CONTENTS

PAGES

ABSTRACT 1

CHAPTER ONE : INTRODUCTION 3

References 6

CHAPTER TWO : THEORETICAL BACKGROUND 8

2-1 The Cross-Section 8

2-1-1 The Reaction Rate 9

2-1-2 Dependence of Cross-Section on Energy ... 12

2-2 Nuclear Reaction Models 15

2-2-1 The Compound Nucleus Model 15

2-2-2 The Direct Reaction Model 16

2-2-3 The Optical Model 17

2-2-4 The Statistical Multistep Direct (SMD) &

The Statistical Multistep Compound (SMC) 18

2-3 The EXIFON Code 18

2-4 The Neutron Activation Technique 19

2-5 The General Equation of Neutron Activation

Technique 21

References 24

CHAPTER THREE : THE EXPERIMENTAL SET-UP 25

3-1 The Neutron Generator 25

3-1-1 The T(D,n)4He Reaction 25

3-1-2 Ion Source 27

3-1-3 Accelerating System 30

3-1-4 High Voltage 30

3-1-5 Beam Transport 30

3-1-6 Tritium Target 30

3-2 Flux Measurements 32

3-3 Checking of The High Voltage 33

3-4 Variation of Neutron Energy With Laboratory

Emission Angle 35

3-5-1 Calibration of the Current Integrator — 61

3-6 Gamma-Ray Spectrometer System 91

3-6-1 Interaction of Gamma-Rays With Matter ... 91

3-6-2 Radiation Detectors 92

3-6-3 The Counting System 92

3-6-4 The Multichannel Analyser (MCA) 95

3-6-5 Efficiency Measurements 96

3-6-6 Efficiency Ratio Measurements 101

3-6-7 Efficiency Measurement of The HPGe

Detector at 15 cm Distance 107

3-6-8 Photopeak Efficiency Measurements of The

HPGe Detector at 0 and 1.2 cm 107

3_6_9 "Total-to-Peak" Efficiency Ratio

Measurements 120

References 124

CHAPTER FOUR : CORRECTIONS USED IN CROSS-SECTION

MEASUREMENTS 126

4-1 Scattered Neutrons 126

4-2 Attenuation of Neutrons in Samples 127

4-3 Correction of The Flux Due to The Distance

From The Target 128

4-4 Correction Due to The Variation of The Flux

With Time 128

4-5 Dead-Time Correction 130

4-6 The Cascade Correction 131

4-7 The Self-Absorption Correction 133

References 162

CHAPTER FIVE : EXCITATION FUNCTIONS MEASUREMENTS:

RESULTS AND DISCUSSION 163

5-1 Experimental procedure 165

5-2 The Excitation Function of Zn(n,p) Cu

Reaction 168

5-2-1 Discussion 179

5-3 The Excitation Function of 64Zn(n,2n)63Zn

Reaction 182

5-3-1 Discussion 189

5-4 The Excitation Function of 51V(n,a)48Sc

Reaction 193

5-4-1 Discussion 20248 48

5-5 The Excitation Function of Ti(n,p) Sc

Reaction 206

5-5-1 Discussion 211

5-6 Conclusion 215

References 217

CHAPTER SIX : INVESTIGATIONS ON THE SYSTEMATICS OF (n,ot)

AND (n,p) REACTION CROSS-SECTIONS AT 14.6

MEV NEUTRONS 220

6-1 Experimental Procedure 221

6-2 Energy Determination of Neutrons Using

90Zr(n,2n)89m+gZr Reaction 225

6-3 Results of Foils Used as Fluence Monitors 229

6-4 The (n,a) Reaction Cross-Section Results 233

6-5 The (n,p) Reaction Cross-Section Results 233

6-6 Discussion 246

References 270

ACKNOWLEDGEMENTS

Firstly, I wish to thank Dr. Farouk Habbani for his

supervision and continuous encouragement.

I would like to express my gratitude to Professor

J. Csikai of the Institute of Experimental Physics, Kossuth

University, Debrecen, Hungary, who gave me invaluable

assistance. Also, my gratitude is extended to Mis A. Grallert

of the same institute for assistance and cooperation.

I also acknowledge with thanks the encouragement and

support given by Dr. Fathi El Khangi, Mr. Omer El Amin and

Dr. Abbashar Gism El Seed of the Atomic Energy Research

Institute.

lam also indebted to Dr. A. Shouak of the Physics

Department, University of Rabat, Morocco, for his valuable

assistance.

I would also like to express my thanks to the staff and

the lab. technicians of the Institute of Experimental

Physics, Kossuth University, Debrecen, Hungary and of the

Physics Department, University of Khartoum for their support

and help.

lam also indebted to my colleagues at the Atomic Energy

Research Institute, for various contributions in this work.

Lastly, I would like to take this opportunity to thank

the International Atomic Energy Agency for their generous

support of granting a one year fellowship in Debrecen,

Hungary in 1992.

(j JJ»'i j j- j ^LaiVl i n nil (JjJall JA-ai (j-» S^ l J (jA ^ j j J j j u l l inj.Vnll <L

(n,a)

<ijj»-»lt

XY

^ ^ »"'" r" j j ^ j j *1 • x-^yl

,<[ . m\

c>

, 48Ti(n,p)48sc,

(n,p)N - Z)/A

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ABSTRACT

The neutron activation technique is one of the main

methods that are used for neutron reaction cross-sections

measurements.

In this work fast neutrons of energy around 14-MeV

produced by the D-T reaction were used.

64 64The cross-sections of the reactions Zn(n,p) Cu,

64Zn(n,2n)63Zn, 51V(n,a)48Sc and 48Ti(n,p)48Sc around 14-MeV

showed large discrepancies in the literature. The excitation

functions of these reactions were measured around 14 MeV

neutron energy, with statistical error not exceeding 7%. The

EXIFON code, based on the statistical multistep compound and

statistical multistep direct nuclear reactions models, was

used to compare the theoretical calculations of the cross-

sections, with the experimental measurements of the the

excitation functions. Good agreement was observed between

calculated and measured data for more than 85% of the cases.

Investigations were also made for the dependence of the

(n,a) and (n,p) reaction cross-sections on the asymmetry

parameter (N-Z)/A and a number of isotopes for each element

studied. In this way it was hoped to improve the systematics

of these cross-sections, which will help in determining the

unknown cross-sections with better accuracy, and will

contribute forwards better understanding of the theory .

Various corrections were applied to the measurements to

improve the precision and accuracy of the results.

CHAPTER ONE

INTRODUCTION

The accurate knowledge of the cross-sections and the

excitation functions of fast neutron reactions are of

interest from the point of view of nuclear reaction theory

(nuclear models), fission and fusion reactor technology, fast

reactor design and control calculations, neutron fluence

monitoring, safeguards, neutron therapy, medical physics,

activation and prompt radiation analysis, radionuclides

production and applications of data in dosimetry.

Measurements of fast neutrons reactions cross-sections were

carried out by various authors [1-8].

In this work the fast neutrons (around 14 MeV energy),

produced by the neutron generators of the Physics Department,

University of Khartoum and Institute of Experimental Physics,

Kossuth University, Debrecen, Hungary, were used for the

various investigations undertaken. The neutron generators

produced fast neutrons by the D-T reaction.

The energy and energy spread of neutrons emitted in this

reaction were determined using Nb/Zr activity ratio

method [ 9 ].

A study was made also on the self-target build-up effect

which results in contamination of the D-T neutrons by the D-D

neutrons. This was done using the associated particle method

(APM) attachment [10,11]. Various materials were irradiated

by a deuteron (D ) beam of energy 100 KeV. The accumulations

of deuterons in these materials were determined by measuring

the net counts of protons emitted from the reaction D(d,p)T.

The results obtained showed that the self-target neutron

background could be decreased to a considerable amount by

choosing the beam stop material properly.

In this work measurements were also carried out of the

64 64excitation functions of the reactions Zn(n,p) Cu,

64Zn(n,2n)63Zn, 51V(n,a)48Sc and 48Ti(n,p)48Sc in the energy

range 13.63-14.73 MeV. These reactions are important from the

point of view of dosimetry reactions, as well as for neutron

fluences and fusion technology. The published experimental

cross-sections for these reactions around 14 MeV show large

discrepancies. Thus it was of interest to attempt

measurements for more accurate excitation functions. These

measured excitation functions were used to check the nuclear

reaction models. The statistical multistep

compound/statistical multistep direct reaction models were

used employing EXIFON code. The calculations were in good

agreement with the measurements, especially for the (n,2n)

reaction.

Some recent measurements of the cross-sections of (n,a)

and (n,p) reactions also showed a significant spread in the

data. Systematic investigations on the cross-sections of

(n,a) and (n,p) reactions were made at a neutron energy of

14.6 MeV to study the effect of (N-Z)/A asymmetry parameter.

Such investigations were carried out by various authors

[1,2,4], but considerable discrepancies still existed. More

accurate knowledge was needed of the different systematics of

cross-sections to be used for the estimate of unknown data

and for the adoption of recommended cross-sections among the

discrepant experimental values.

In this work the cross-section measurements were done

applying the neutron activation technique and using the

relative method, with simpler calculations and hopefully more

accurate and precise results. Also, an advanced computer

programme for gamma spectrum analysis called GANAAS, supplied

by the International Atomic Energy Agency, was used to fit

the areas of the peaks in the various gamma ray spectra.

Various corrections were carried out for the

measurements in this work, including: self-absorption, dead-

time, cascade coincidence, flux depression and flux variation

in time. In this way it was hoped to further improve the

precision and accuracy of the measurements.

J

REFERENCES

1- "Handbook of Fast Neutron Generators", J. Csikai, CRC

Press Inc. Boca Raton, Florida, 1987.

2- J. Csikai, Proc. Int. Conf. On Nuclear Data For Science

and Technology, Antwerp, ed. K. H. Bockhoff, Reidel,

Dordrecht, 1983.

3- "Handbook of Of Nuclear Activation Data", Z. Body,

Technical Reports Series No. 273 IAEA, Vienna, 1987.

4- Proc. Int. Conf. On Nuclear Data For Science and

Technology, Julich, ed. S. M. Qaim, Springer-Verlag,

Berlin, 1992.

5- N. I. Molla and S. M. Qaim, Physical Review C, 45, No. 6

June 1992, p3002.

6- "Handbook On Nuclear Activation Cross-Sections", The IAEA,

Technical Reports Series No. 156, Vienna 1974.

7- J. Csikai, Recent Trends In The Use Of Neutron Generators

In Industrial and Basic Research, First National Conf. On

Nuclear Methods, Zaria, Nigeria, Sept. 2-4, 1992.

8- J. Csikai, Z. S. Lantos, Cs. M. Buczko and S. Sudar, Z.

Phys. A-Atomic Nuclei 337, 39-44, 1990.

9- J. Csikai, The Properties of D-D and D-T Neutron Sources,

IAEA Interregional Training Course On Neutron Generators,

Leningrad 25 Sept.- 29 Oct. 1989.

10- J. Csikai, Determination of Average Energy and Energy

Spread of Particle Beams, IAEA Consultants' Meeting on

Utilization of Low Energy Accelerators, Debrecen, 1-5

June 1992.

11- M. Drosg, Sources of Variable Energy Monoenergetic

Neutrons for Fusion Related Applications, Nuclear Science

and Engineering, 106, 279-295, 1990.

CHAPTER TWO

THEORETICAL BACKGRUOND

2-1 The Cross-Section:-

The cross-section is a quantitative measure of the

probability with which nuclear reactions and other collision

processes occur [1].

Consider an incident collimated beam of particles

impinging upon target nuclei in a suitable specimen of

material and interacting with them through the processes of

scattering, absorption and/or reaction, thereby becoming

attenuated. The attenuation may be in intensity or energy, or

both, by an amount which can be determined by measurements

effected on the emergent beam. The most naive way of

picturing the likelihood of interaction is to visulize the

incident beam as made up of point particles which if they

directly strike some part of a target nucleus, set up an

interaction, whereas if they miss the target nucleus, they

proceed unaffected. However, this naive conception overlooks

both the finite extention of the impinging particles and the

finite interaction radius which may be presumed to extend

quite some way beyond the immediate confines of the target

nucleus. Hence rather than treating the geometrical cross-

sectional area of a nucleus ( TTR ) [where R is the nucleus

8

radius] as a measure of interaction probability, it is

meaningful to ascribe to each nucleus an effective area a

perpendicular to the incident beam such that if a bombarding

particle impinges upon any part of such an imaginary disk, a

reaction will occur, but otherwise no interaction takes

place, as seen in Fig[2.1]. The magnitude of the disks cross-

section a depends upon the reaction and upon the energy of

the incident particles. Its size is suitably expressed in

units of barns, (1 barn=10~24 cm2 ).

2-1-1 The Reaction Rate:-

Consider a collimated beam of monoenergetic particles

impinging upon a specimen of rectangular shape of area F

normal to the beam and thickness d, as shown in Fig[2.2], if

the total number of target nuclei is n then the number of

target nuclei per unit volume, is

n'= n/Fd (2.1)

For a thin target d is considered sufficiently small,

with no overlapping or masking of the individual nuclei.

The overall area then presented as target is no and the

probability for an impinging particle to give rise to a

reaction is thus

P = na/F = n'ad (2.2)

incidentbeam o

Fig [2.1] Interacion of incident beam with nucleus effecive area

10

incidentbeam

target

Fig [2.2] Monoenergetic beam of particles interact withthe effective area of the nuclei in rectangularsample

I I

If the number of incident particles per second is NQ , the

reaction rate, or the number of reactions per second, is

R = PNQ = NQ n'ad (2.3)

In the case of thick target the reaction rate R is given by

the formula

R = NQ [l-exp(-n'ad)] (2.4)

if d is small, this reduces to the thin target expression

(2.3) [2].

2-1-2 Dependence of Cross-Section on Energy:-

The cross-sections for various nuclear reactions depend

on bombarding energy in a highly individualistic manner. The

detailed dependence of cross-section on bombarding energy is

often called the " excitation function " for the particular

reaction.

The theories of the cross-section of nuclear reactions

in which a compound nucleus is formed are divided into two

broad classifications. At low bombarding energies the excited

levels of the compound nucleus are discrete and may be widely

spaced. Here the reaction cross-sections are described by a

resonance theory. At higher bombarding energies the excited

levels in the compound nucleus are more closely, and

12

partially overlapped. In this energy domain, the so called

continuum theory undertakes to describe the general variation

of cross-section with bombarding energy [3].

The energy dependence of nuclear cross-sections,

averaged over individual fluctuations and resonances, is

expressed in terms of two parameters of the inner nuclear

structure. Consider the case of incident neutrons. The two

parameters are the nuclear radius R and the wave number K of

the incident neutron after it is in the interior of the

compound nucleus. The wave number K for the neutron within

the nucleus becomes:

K2 = KQ2+k2 (2.5)

where k is the wave number of the incident neutron as it

approaches the nucleus and KQ is the interior wave number if

the bombarding energy is zero. Under the assumption of

constant density in nuclei, KQ does not depend upon the mass

number A. It needs to be emphasized that R denotes a distance

at which the wave number of the incident neutron changes from

it's value k outside the nucleus to the value K inside the

nucleus. The change actually takes place over a finite

distance of the order of 1/K [4].

The total cross-section, reaction cross-section and

scattering cross-section are expressed in units of 7rR2:

13

CTtot,sc,r

The three functions Ftot' Fsc' Fr' d e P e n d only on the

dimensionless variables x = kR, and XQ = KQ R.

At large energies, where r = 1/k << R (where r is the

de-Brglie wavelength/2n of the incident wave) the reaction

and scattering cross-sections for neutrons both approach the

same asymptotic value

CTr = °sc

Therefore the total cross-section, for high-energy neutrons,

becomes:

°t = CTr + asc

and at low energies the ar shows a 1/v dependence where v is

the neutron velocity [4]. Equation (2.7) for the high energy

neutrons reaction cross-section, becomes for small energies

[4kK/(k+K)2] (2.9)

where the quantity in the square brackets is the usual

expression for the transparency of the potential step at the

surface of the nucleus. For very small bombarding energies,

! k << K and R << r = 1/k, so that the reaction cross-section

would be approximately

14

ar w 47r/kK for r » R (2.10)

These simple relationships imply a monotonic variation of

total cross-section between

a. « 27r(R+r)2 for large energies

and a t « 4jr/kK for very small energies [3]

2-2 Nuclear Reactions Models:-

A nuclear reaction is an intricate process of

; rearrangement of an atomic nucleus. As in the case of nuclear

structure, it is practically impossible here to obtain a

precise solution of the problem. Various nuclear models were

proposed to account for the various nuclear reaction

mechanisms.

2-2-l_The Compound Nucleus Model:-

; This model was introduced by Niels Bohr (1936),r-

\ according to which the reaction takes place in two stagesV

£ with the formation of an intermediate nucleus, C called the

L compound nucleus:

a + A > C > b + B (2.11)

it

\ The compound nucleus concept is applicable only in the case

when the life time of the compound nucleus is long enough ( ~

—1410 s e c ) , which is much longer than the characteristic

15

— 21

nuclear time ( « 10 sec.) [5].

Reaction that takes place via a compound nucleus can be

subdivided into the resonance and the nonresonance types.

If the widths of the compound nucleus levels are smaller

than the spacing between them, then, in the case of a fixed

energy of the incident particles the reaction can take place

only via a single level. The reaction cross-section vs.

energy dependence will be of a resonance type. Accordingly,

such reactions are called the resonance reactions.

If the distribution of the levels is so dense that the

spacing between them are less than their widths, so that

practically they merge, then in this case the reaction will

take place at any energy. Such reactions are called

nonresonance.

The cross-section of the compound nucleus reaction of

the type given by equation (2.11) can then be represented in

the form of a product of two multipliers: the cross-section

CTQ of the formation of the compound nucleus by particle a and

the probability IV of the decay of the compound nucleus by

way of the b channel [5].

2-2-2 The Direct Reaction Model:-

This is used if the time of interaction between the

projectile particle and the nucleus does not exceed the

characteristic nuclear time. In this case the projectile

effectively collides with one or two nucleons of the nucleus

16

practically without contacting the others or near the surface

of the target nucleus.

In the direct processes the particles escaping from the

target nuclei may be individual nucleons, nucleon pairs,

deuterons, He2 nuclei, alpha particles as well as more

complex nuclei such as lithium, beryllium, etc. Direct

reactions are classified into various types depending on the

nature of the incident and outgoing particles. [5]

2-2-3 The Optical Model:-

The optical model treats the nucleus as a continuum that

refracts and absorbs the de Broglie waves of the incident

particles. Quantum mechanics shows that the part of the

refractive index for a de Broglie waves is played by the

Hamiltonian of interaction of the particle with the force

field of the nucleus. To describe absorption, an imaginary

part iw is added to such Hamiltonian, so that it assumes the

form

Hin = V ( r ) + i W ( r ) (2.12)

where V(r) is the Hamiltonian. Hence, in the optical model

the interaction between the impinging nucleon and the nucleus

is approximated by the scattering and absorption of this

nucleon by a force centre.

The optical model describes the differential and the

17

integral elastic scattering cross-section at various energies

of scattered nucleons, and the cross-section of all inelastic

processes i.e. the absorption cross-section of the nucleons

by nuclei. In the energy range 10 - 20 MeV, where the

contribution of direct processes is relatively small, the

absorption cross-section coincides with the compound nucleus

formation cross-section.

The limiting case of the optical model is the model of a

blackbody in which the nucleus is presumed to absorb all

particles that had struck it [5].

2-2-4 The Statistical Multistep Direct (SMD) and The

Statistical Multistep Compound (SMC):-

The (SMD) and (SMC) mechanisms describe the equilibration

of the composite nucleus through a series of two-body

collisions which eventually may lead to the formation of a

compound nucleus. By definition, the (SMC) mechanism involves

only bound configurations embedded in the continuum, yielding

angular distributions symmetric about 90 degrees center of

mass, and is expected to be relevant mostly at relatively low

(10 - 20 MeV) incident energies [6].

2-3 The EXIFON Code:-

Using the nuclear reaction models the reaction cross-

section could be calculated.

In this work EXIFON computer code was used. The EXIFON

18

I code is based on an analytical model for a statistical

f multistep direct and multistep compound reactions (SMD/SMC

models). It predicts emission spectra, angular disributions,

and activation cross-sections, including equilibrium,

preequilibrium, as well as direct (collective and non-

' collective processes). Multiple particle emissions are

considered up to three decays of the compound system. The

: model is restricted to neutron, proton, and alpha induced 4i

- reactions with neutrons, protons, alphas, photons in the

outgoing channels. The range of validity; target mass number

A > 20, and bombarding energies below 100 MeV [7].

2-4 The Neutron Activation Technique:-

The neutron has charge zero and mass 1.008665 amu.

In the absence of other nuclear ' matter, a free neutron

disintegrates with a half-life of about 12.5 min into a

proton, an electron and neutrino by the reaction

n > p+e~ +v' (2.13)

Many of the properties of neutrons depend on their

kinetic energy. Neutrons may be arbitrarily classified

according to their energy as follows:

1) Slow Neutrons:- neutrons with energies up to 1 KeV.

The most important subgroup of this class is the

"thermal" neutrons with energies about 0.025 eV.

19

Another important subgroup of slow neutrons is the

epithermal neutrons with energies in the range 1 eV -

1 KeV.

2) Intermediate Neutrons:- neutrons with energies

between about 1 to 500 KeV.

3) Fast Neutrons:- neutrons with energy above 0.5 MeV.

When a neutron interacts with a target nucleus a

compound nucleus is formed. The compound nucleus has a

certain finite life-time during which it remains in highly

excited state. De-excitation of the compound nucleus can

occur in different ways that are independent of the way the

compound nucleus was formed. Each of these processes, shown

in equation (2.14), has a certain probability, depending on

the nuclear cross-section of each mode, which is related to j

the excitation energy of the compound nucleus [8]. In theI

following relation the various ways by which a compound !

nucleus can disintegrate are shown, when neutrons interact ,i

with a target nucleus X: j

I > elastic scattering

| > inelastic scattering j

| > emission of particles (2.14)

X+n > [CN]* H (n,a),(n,p),(n,2n), etc.-> radiative capture (n,r)

1 — > fission (n,f)

The resulting product nucleus may be radioactive or stable.

The radioactive nuclide formed has a characteristic

20

half-life, mode of decay and emitted energy [8].

Measurements of gamma rays emitted from the radioactive

nuclide have, in general, much wider applications in neutron

activation technique, because gamma rays emitted from most

radionuclides have a wide range of energies (40 - 1000 KeV),

with relatively high penetrating power. Thus gamma rays are

subjected to minimal losses by absorption in a sample during

their measurements. This property, coupled with the recent

developments in high-resolution and high effeciency

semiconductor detectors, makes the neutron activation

technique in the reaction cross-scetion measurements through

gamma ray spectroscopy a powerful technique.

2-5 The General Equation of Neutron Activation Technique:-

Let N be the number of radioactive nuclei produced

during irradiation time t, a be the cross-section of the

reaction, <f> the neutron flux, n number of target nuclei and r

the decay constant of the radionuclide formed. Then we have

the following differential equation

dN/dt = <fion - TN (2.15)

where the first term on the R.H.S. describes the increase of

N because of the activation process, while the second term

given the decrease of N due to decay.

The general solution of such differential equation is :

N = exp(-rt)[c + an 0(t) exp(rt) dt] (2.16)

Where the flux 0 is assumed to be time-dependent and C is a

constant of integration. However, if the flux is constant,

i.e 0 = 0 Q and assuming the initial condition N=0 at t=0,

then we have

N(t)= 0 Q an/r (l-exp(-rt)) (2.17)

The activity at time t will be

A(t)= TN(t)= 0 n an(l-exp(-rt)) (2.18)

After the end of the irradiation, A decreases exponentially

and after a time t- following end of irradiation we have :

= A(t) exP(-r(t1-t)) (2.19)

If the activity measurement is performed during the time

interval between t. and t_, then the expected number of decay

| events A will be given by :

Ac=0Qan/r (l-exp(-rt))exp(-r(t1-t2))(l-exp(-r(t2-t1)) (2.20)

where, t=t. is the irradiation time, t--t=t is the waiting

time and t2~t, =t is the counting time. Accordingly equation

(2.20) can be written as

22

Ac =0oan/r (l-exp(-rti))exp(-rtw)(l-exp(-rtc)) (2.21)

Clearly, the average number of counted decay events N will

be less than A due to different effects such as the

effeciency of the detector e for the particular energy and

for the particular counting geometry, and the intensity of

the measured gamma line I so :

N c =elr Ac (2.22)

Also the number of target nuclei is given by :

n= N /A. mf (2.23)

where m = mass of the element in the sample, A t = atomic

23weight of the element, N = Avogador's number= 6.02 x 10Cl

mol~ , f = the relative isotopic abundance of the target

isotope.

From the equations (2.21) and (2.22) we have for the

basic equation of the neutron activation technique :

(l-exp(-rti))exp(-rtw)(l-exp(-rtc)) (2.24)

23

REFERENCES

1- "Introduction to Experimental Nuclear Physics", R.M.

Singru, Indian Institute of Technology, Kanpur, 1974, pl9.

2- "Physics of Nuclei and Particles", Pierre Marmier and Eric

Sheldon, Federal Institute of Technology, Zurich, 1969,

p68-75.

3- "The Atomic Nucleus", Robley D. Evans, Massachusetts

Institute of Technology, 1955, p441.

4- H. Feshbach and V.F. Weisskopf, Phys. Rev. , 76 (1949)

1550.

5- "Nuclear Physics", Yu.M. Shirokov and N.P. Yudin, Mir

Publishers, Moscow, Vol.1 (1982), pl35-160.

6- M. Herman, G. Reffo and H.A. Weidenmuller, Nucl. Phys.,

A536 (1992) 124-140.

7- "EXIFON-Statistical Multistep Reaction Code", H. Kalka,

Techniche Universitat, Dresden, May 1990.

8- "Radiation Physics", T. El Nimr, Tanta University, Egypt,

1983.

24

CHAPTER THREE

THE EXPERIMENTAL SET-UP

3-1 The Neutron Generator :-

Neutron generators using low energy deuterons are used

: to produce neutrons mainly via two reactions: D(d,n) He with

\ Q-value of 3.25 MeV and T(d,n)4He with Q-value of 17.5 MeV.

The latter type of neutron generator used in this work.

3-1-1 The T(dfn)4He Reaction :-

The importance of this reaction is that it produces

monoenergetic neutron beams over the energy range of 13.6-

14.8 MeV. The properties of this reaction are summarized in

table [3-1].

3 4The most important feature of the H(d,n) He reaction in

practice is the resonance at a deuteron laboratory energy of

about 107 KeV which reaches a peak cross-section of about 5

barn. The high yield of neutrons from this reaction at low

input energies, lends itself to important and diverse

applications [1].

The high Q-value of 17.59 MeV enables neutrons with

energies of about 14 MeV to be produced at forward laboratory

angles using low energy accelerators.

3 4The neutrons from the H(d,n) He reaction decrease in

energy with increasing angle of observation relative to the

25

Table [3-1] Some properties of the D-T reaction.

ReactionMeV

3H(d,n)4He

Q-valueMeV

+17.59

Break-upreaction

3H(D,np)3H

3H(d,2n)3He

Q-valueMeV

-2.225

-2.952

ThresholdMeV

3.71

4.92

E (max.)MeV

15

[1]

26

incident deuteron beam, but they are monoenergetic at a fixed

angle [1].

The unfolded spectrum of neutrons produced in the

3H(d,n)4He reaction at E d = 150 KeV is shown in Fig[3-1].

The neutron generator is commercially available under

different shapes and constructions. In principle a neutron

generator is composed of an ion source and an accelerating

tube, ending in a drift tube closed by the tritium target.

The deuteron beam is completely stopped in the target.

As the accelerator has to operate under vacuum, the

system is evacuated by means of a suitable pumping system.

Fig[3-2] shows schematic features of the neutron generator.

3-1-2 Ion Source :-

In the ion source which is filled with deuteron gas at

low pressure a plasma is formed by the energy that is

transferred to the gas by a radiofrequency oscillator of

about 60 to 100 MHz, coupled capacitively or inductively to

the source. In the plasma several types of ions are formed of

which the most numerous are D and D o ions. The ions formed

in the ion source are extracted by the voltage applied to the

extraction electrode, through the thin ~1 mm extraction canal

into the accelerating tube.

The regulation of the deuterium gas supply into the ion

source is usually achieved by leakage through a heated

palladuim tube [3] [4].

27

0.0

>u

U

ciEu

\c10

a

X

0 . 8

0 . 8

0 .4

0 . 2

i

D-T

•

-•

1 ' 1

reaction

4 6 8 10 12

NEUTRON ENERGY (tfoV)

1-t 18

3 AFig[3-1]: Unfolded spectrum of neutrons produced in H(d,n) He

reaction at E :«• T50 KeV (Ref.2).d

Extraction R.F. Power Supply

0-5KV,«ve

Ion source tase

0-10 KV.^ie

Ion source bottle

Ground

/Drift lube

««<L/^ T a r g e t

Conal

lo vacuumAccelerating pumpelectrodes

Fig [3-2] Neutron Generator Schematic Features

29

3-1-3 Accelerating System :-

The accelerating system consists of the accelerating

tube and the voltage divider that feeds the individual

electrodes in the tube (usually 10) with equal voltages of

about 15 KV. The accelerating tube is a series of metal

electrodes separated by porclain or aroldite isolators [3].

3-1-4 High Voltage :-

The high voltage supply has to provide the requested

high voltage and the current that will cover the maximum

current delivered by the ion source and provide for losses

incurred in different parts.

3-1-5 Beam Transport :-

At the end of the acceleration the beam is transported

through the evacuated tube for shorter or longer distances.

The beam will have the natural tendency to spread out so that

the beam transport is usually fitted with magnetic or

electrostatic lenses to refocus the beam on the tritium

target. A focusing lens (gap lens) is usually inserted in

front of the acceleration electrodes for such a purpose (see

Fig[3-2]).

3-1-6 Tritium Target :-

The tritium target is obtained by adsorbing tritium on a

thin metal layer that has been evaporated on a usually

30

thicker Cu or Mo backing. For the thin metalic layer titanium

or zirconium is mostly used [3]. The taitanium is impregnated

with 1.5 tritium atoms per one titanium atom. Such a target

is stable for temperature upto 250 °C. The advantage of this

TiT solid target is the absence of a window, which results in

much better energy resolution if low-energy beams are used.

The main disadvantage of the TiT solid target is the strongly

reduced specific yield due to the other constituent in the

active volume of the target. In addition the areal density of

the tritium is not uniform over the target area, so the

neutron yield will depend on the beam spot position [5].

The degradation of the target during exploitation is

caused mainly by overheating. It is therefore necessary to

cool the target. Usually clean water is used for cooling.

However, for scatter-free cross-section measurements the

cooling may be done using air jet to remove the heat from the

backing.

By repeated bombardments the tritium in the target is

depleted and a half-life can be defined as the time which is

necessary to obtain half of the original neutron output at a

constant beam current. The half-life is influenced by many

parameters. However, one can accept that a typical half-life

is in the order of 1 hour for a beam current of 1 mA. The

life-time of a target can be extended by rotation of the

target in which tritium is deposited in annular form. A

typical neutron yield for an "open" type neutron generator,

31

with a new target is of order of 10 n/s.mA [4].

Neutron output of this order requires appropriate

shielding for the safety of the personnel. Typical

thicknesses of concrete walls are of the order of 1 - 2

meters.

3-2 Flux Measurement: :-

From equation (2.24), the flux can be given by the

expression :

0=NarAt/Namfaeeslr(l-exp(-rti))exp(-rtw)(l-exp(-rtc)) (3.1)

where e is the photopeak efficiency of the gamma line taken

from equation (3.28) and e is the self-absorption corrections

of the gamma line counts.

An Al-foil of mass 0.1744 g was used, it was irradiated

at the target of the generator, for irradiation time of 600

sec, the waiting time was 600 sec, and the collecting time

was 600 sec. The generator was operated at 125 KV and 600

The results obtained :

(N)1 3 6 g= 4032, a =113.7 mb =0.1137 X 10~ 2 4 cm2,

e =0.008843, e =0.998, I =1, r =1.28333 X 10~5 sec"1,S T

t^ =tw =tc =600 sec, Afc =27, N a =6.02 X 102 3 mole"1, f =1

The. flux <(> =2.323 X 108 n/cm2.sec.

32

3-3 Checking of The High Voltage:-

The energy of the emitted neutrons in the neutron

generator is dependent on the energy of the incident

deuterons, which is controlled by the high voltage of the

neutron generator. The high voltage meter is expected to

indicate the energy to which the deuterons have been

accelerated. Thus checking the calibration of the high

voltage is important to ensure correspondence between the

meter reading and the energy of the deuterons.

The use of resonant nuclear reactions for calibrations

of low-energy accelerators is one of the most reliable

methods [6].

One of the reactions commonly used for the calibration

of the high voltage of the neutron generator is

11B(p,T)12C (3.2)

This reaction has a resonance at a proton energy of 163

KeV, at a cross-section of 0.16 mb. The energy of the emitted

prompt gamma is 4.4 3 MeV, with 96.5% emission per reaction

[7], Several other resonant (p,r) reactions, with suitable

resonance energies, would be needed for the full calibration

of the high voltage of the neutron generator. We have decided

to check the calibration of the high voltage at one point,

using the above reaction, with resonance energy at 163 KeV.

The experimental arrangement for such a measurement is

shown in Fig[3-3]. A measurement for the reaction B(p,r) C

33

Boron target

-4-P-beam

8 X8 cm Nal detector

Fig [3-3] Experimental setup for checking the high voltage

calibration

34

was performed. For prompt gamma detection a 8X8 cm Nal(Tl)

detector was used. The peak areas of the 4.43 MeV prompt

gamma line for 5 mins counting at various high voltage

settings of the neutron generator are shown in table [3-2].

The variation of the counting rate in cpm versus the

high voltage of the neutron generator is shown in Fig[3-4].

If the resonance position is defined at 50% of the

counting-rate, then it is found to occur at a high voltage of

163 KV i.e 163 KV corresponds to a proton energy of 163 KeV

which is the known resonance energy for such a reaction. No

further (p,T) reactions were performed. However, the

measurement confirmed the good correspondence between the

high voltage readings and the energy of the deuterons.

3-4 Variation of Neutron Energy with Laboratory Emission

Angle :-

The accurate knowledge of the energy, energy spread and

angular distribution of neutrons emitted in the D-T reaction

is needed for the precise measurement of cross-sections

around 14 MeV. It is then possible to estimate the

contribution of reaction having different thresholds to the

activity of a sample and to make distinction between the role

of the possible interfering reactions through their energy

dependence. The excitation functions for many reactions vary

significantly around 14 MeV neutron energies. Therefore, it

is important to place the samples in well defined positions

35

Table [3-2] Variation of the high voltage with prompt

11 12gamma counting-rate from B(p,r) C reaction

N.G. H.V.(KV)

170165160155150140130

peak areain 5 mins

2755197978438686420

counting-rate(cpm)

551395.8156.877.217.28.40

36

o

td

oo

600

500

400

300

200 -

100 -

020 I 60 180

high voltage (K.V.)Fig [3 -4 ] Variation of the H.V. with c o u n t i n g - r a t e for

11 12prompt gamma from B(P,7) C reaction

200

with regard to the direction of the bombarding deuteron beam,

both for neutron activation analysis and neutron nuclear data

measurements.

The energy of neutrons emitted in the D-T reaction can

be given in the laboratory system for the nonrelativistic

case [E, < 20 MeV] by the following equation [6]:

COS6+(2.031 E d COS 9 +352.64228+9.

5.01017(3.3)

where E, and E are energies of incident deuteron and emitted

neutron in MeV, respectively, and 6 is the neutron emission

angle relative to the deuteron beam.

Measurements were carried out for the energy and angular

distribution of neutrons for the neutron generator in the

Physics Department, University of Khartoum. These

measurements were based on the fact that the (n,2n) cross-

90section for Zr varies rapidly with neutron energy around 14

93MeV, while the (n,2n) cross-section for Nb shows negligible

change. This is shown in Fig[3-5] [6]. Therefore, the neutron

energy versus emission angle can be determined by measuring

the ratio of the Zr and 9 Nb specific activities (A/m)

produced by the D-T neutrons at different angular positions

[6]. The nuclear data for these two reactions are shown in

Table [3-3].

38

WITHOUT ATTENUATION

050 150 180

F.MISSON ANGLE

Fig[3-5]: Comparison of the excitation functions of90

93and Nb(n,2n) reactions around 14 MeV neutrons.

90,Table [3-3]: Nuclear data for the (n,2n) reaction of Zr

and Nb [8]

reaction

93Nb(n,2n)92mNb

90Zr(n,2n)89Zr

10.143 d

78.438 h

ET (KeV)

934.5

909

zr %

99.1

99

40

The experimental arrangement of the samples around the

T-target is shown in Fig[3-6]. The Zirconium samples and Nb

fluence monitor foils were placed back-to-back and fastened

to an Aluminium support ring of 12 cm diameter, with the beam

spot diameter of 0.5 cm. Neutrons between 13.4 and 14.6 MeV

were produced by the D -beam of 125 KeV energy in a

scattering free arrangement. For target cooling air jet was

used (rather than the usual water cooling) to reduce

scattering.

The rectangular-shaped Zr and Nb foils of dimensions2

15X10 mm were placed at the angular positions shown in Table

[3-4], with respect to the direction of the D beam.

The foils were irradiated for 55 min each using a high

voltage for the neutron generator of 125 KV and a target

current of 100 ph. The intensities of the 909 KeV and 934

KeV gamma lines emitted in the decay of Zr and mNb,

respectively, were measured by a HPGe detector operated at a

bias of +2000 Volt. Typical gamma-ray spectra obtained are

presented in Fig[3-7].

The relative method was used for the determination of

the neutron energy-angle function by the Zr/Nb activity ratio

technique. In this method the activities for the Zr and Nb

samples as a function of angle and the ratios to those

obtained at 90° were taken for the determination of the

neutron energy. The specific activity ratios at the end of

irradiation for both Nb and Zr are given by :

41

airjci

[f-beam

Fig[3-6J The experimental arrangement for neutron energyVs. emission angle measurement

42

Table [3-4]: Angular positions of the samples with respect

to the D beam.

Zr & Nbsamples No.

angle(degree)

1

0

2

40

3

70

4

90

5

110

6

130

7

172

43

O

(0c<uua•H<u•H

s

t Nb+Zr

ch. no.

Fig[3-7]: Spectrum of Nb+Zr using HPGe detector

(3.4)

As,Zr ( e ) / As /Zr( 9 O° ) = 0 ( e ) / 0 ( 9 o O ) X aZr [ En ( e ) ] / aZr [ En ( 9 O° ) ] ( 3' 5 )

From equation (3.5) and (3.6) :

aZr[En(e)] .(e)

a_[E r90°)=14.08 MeV]UL n

s,Nb (90°)

As,Nb<9>

= R[En]

(3.7)[9]

In equations (3.4) and (3.5) it was assumed that:

oN.[E]=constant. The samples were irradiated simultaneously

for the same time which was much shorter than the half-lives

of the 89Zr and 9 2 mNb isotopes.

The specific activity A is given by:

= Nr/[(exp(-rt.)-exp(-rt,))m] (3.8)

where N is the net area under the gamma peak, r is the decay

constant, m is the mass of the foil, t1 is the time between

end of irradiation and start of counting (cooling time, t )

and t~ is the time between end of irradiation and stop of

counting (t +t t- ) [9]. The results obtained are shown

in Table [3-5].

From equation (3.7) the ratio of the cross-section of

Zirconium at different angles to the value at right angle is

given by:

45

Table [3-5]: Results for the specific activities ratios measurements for Zr and Nb samples.

sampleMo.

1

2

3

4

5

6

7

angle(degree)

0

40

70

90

110

130

172

area of909 peak

394

1053

655

1358

1457

505

1467

area of934 peak

286

1389

688

1375

1721

623

1877

0

82.92

47.85

23.75

34.82

59.38

8.45

2.03

95.45

53.98

34.78

47.77

64.97

23.62

mass ofZr-foils

gm

0.5067

0.4978

0.5038

0.5049

0.5018

0.5024

0.5002

mass of

Mb-foilsgin

0.7462

0.7456

0.7366

0.7369

0.7542

0.7442

0.7445

As,Zr

378.614

371.19

332.614

333.852

322.82

250.45

222.606

As,Nb

195.292

191.694

176.161

183.875

198.204

178.789

173.951

fts,Zr

Rs,Nb

1.93871

1.9364

1.88813

1.81565

1.62873

1.40000

1.27971

gZr[En(e)]

Using Table [3-5] we have :

.(e)

aZr[E (9)] A (9)— ^ — - = 0.5824 X — ^ ^ (3.10)

The results obtained are shown in Table [3-6]. By

fitting these results the following equation was obtained :

2nR= a_ +a^ cos9 +a_ cos 9 (3.11)

where

aQ = 0.9929555

ax = 0.2272351

2 = -0.03321706

The graph which shows these results is given in Fig[3-8].

The parameters a~, a., and a_ were used to calculate the

cross-section ratio of Zirconium at the angles 0°, 10°, 20°,

30°...,180°. The results obtained are shown in Table [3-7],

On the basis of the recommended a(E ) curve for

90 8 9

Zr(n,2n) Zr shown in Fig[3-9] [10] the following equation

was used for fitting :

47

Table [3-6]: Results for the relative cross-section

for Zr at various emission angles

angle(degree)

0

40

70

90

110

130

172

aZr[En(9)]/aZr[En(9)] =R

1.19 ± 0.07

1.13 ± 0.04

1.10 ± 0.06

1.00 ± 0.05

0.949 ± 0.036

0.815 ± 0.077

0.745 ± 0.035

48

1 Of:

[V)

I.

1.08

0.90

0.54

—i

0

| o measured

calculated

18036 72 108 144

emission angle (degree)Fig[3-8] Zr-Nb cross-section i atio Vs. emission

angle

Table [3-7]: The calculated relative cross-section

for Zr at angles from 0° to 180°

angle(degree)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

cross-sectionratio

1.187

1.185

1.177

1.165

1.148

1.125

1.098

1.067

1.031

0.993

0.952

0.911

0.871

0.833

0.799

0.771

0.750

0.737

0.733

50

tOO r-j t r

100

700

too

»0

_, , r

i . i i .

1J.SI .

300

e

to

- 2 2 W . A

o, . 17*.32

u

90 89Fig[3-9]: Cross-section curve of Zr(n,2n) Zr reaction Vs.

the neutron energy.

a[En] = (3.12)

where

aQ = -13244.5

a± = 1668.16

ao = -48.543

and E is the neutron energy [10].

The above parameters and equation (3.12) were used toQ 0 8 9

calculate the cross-section of Zr(n,2n) Zr at different

neutron energies. The cross-section ratios of a[En(8)] toa[En(90°)], where

E n = 14.08 MeV and

CT[En(90°)] = 619.715 mb [10]

were calculated, and the results obtained are shown in Table

[3-8].

Plotting the neutron energy E versus the cross-section

ratios of Table [3-8] a curve was obtained as shown in Fig[3-

10].

Table [3-7] and Fig[3-10] were used for the

determination of the neutron energy at different emission

angles. The results obtained are given in Table [3-9].

The neutron emission angle versus the neutron energy

given in Table [3-9] were fitted to the following eguation :

= a cose +a2 cos 6 (3.13)

52

Table [3-8]: Results for the cross-section ratio

a[En(9)]/a[En(90D)]

E n (MeV)

13.2

13.4

13.6

13.8

14.0

14.08

14.1

14.2

14.4

14.6

14.8

15.0

a[ER] mb

317.078

392.460

463.963

531.576

595.311

619.715

625.724

655.162

711.127

763.207

811.409

855.724

cross-sectionratio

0.512

0.633

0.749

0.858

0.961

1.00

1.01

1.057

1.148

1.232

1.309

1.381

53

o

r

o o

Mft!

—

O

C 2 J^

CD

oc

en |_O5 !

cross-section ratio

o obe o

1

- I

~<C

Table [3-9]: The results for neutron energy versus

neutron emission angle

angle(degree)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

cross-sectionratio

1.200

1.185

1.177

1.165

1.148

1.125

1.098

1.067

1.031

0.993

0.952

0.911

0.871

0.833

0.799

0.771

0.750

0.737

0.733

neutron energyEn(9°) (MeV)

14.54

14.51

14.48

14.45

14.41

14.38

14.30

14.23

14.15

14.06

13.98

13.90

13.83

13.75

13.70

13.64

13.60

13.58

13.57

55

where

aQ = 14.0598694

a± = 0.474051622

a2 = -0.01409443

and E the neutron energy and 9 neutron emission angle. The

graph shown in Fig[3-11] was obtained.

The results obtained were compared to the measurements

done in reference [6], The eguation of the variation of the

neutron energy to the neutron emission angle at deuteron

energy 125 KeV in reference [6] is

E n = E Q +E1 cosG +E2 cos 9 (3.14)

where EQ = 14.0617

E± = 0.6283

E 2 = 0.0149

E n neutron energy and 9 the neutron emission angle.

By plotting the neutron energy versus neutron emission

angle obtained from the eguations (3.13) and (3.14) the graph

shown in Fig[3-12] was obtained. The results show good

agreement between the two measurements.

56

"T"14.7?

14.40

14.08

1 3 . 7 6 ••

3.44

-o-

O measured

fitted

0 36 108 144emission angle (degree)

72 180

Figf'3 1 1 ] Energy of neutrons Vs. emission angle

>

&0

16.0

5.5

15.0

14.5o o

f • D

a 14.0w

13.5

0)

13.0

12.5 -

o o• B

12.0 L

0

QO

• measured

O Ref 6

8 8 g • D nu o o o

8036 72 108 144Emission Angle (degree)

Fig[3—12] Comparison of measured and Ref. [6] results

3-5 Accumulation of Hydrogen in Different Elements:-

Production of monoenergetic neutrons with least possible

spread is highly desirable in nuclear cross-section

measurements. One of the practical effects which influence

the degree of monochromaticity of the neutron beam emitted

from D-T targets is the contamination of primary neutron beam

by neutrons produced by the self-target build-up by

implantation of deuterons into the TiT target leading to the

D-D reaction [5]. Such self-target effect may also occur in

materials surrounding the target such as beam stop.

Measurements were done to study the implantation of

deuterons in different materials using the neutron generator

at the Physics Department, University of Khartoum.

To study the accumulation of deuterons in various

materials the following reaction was used [11] :

D(d,p)T (3.15)

with a Q-value of 4.03 MeV, which is distributed mainly as

3.048 MeV for the emitted protons and 0.984 MeV for the

emitted tritons at 90° and at 100 KeV deuteron energy [5].

The accumulation measurements were carried out using the

experimental set up shown in Fig[3-13]. An associated

particle method (APM) attachment was used. The sample

collimators and Si surface barrier (SB) detector were under

vacuum. A thin Al foil was placed on the face of the

59

••mpla

D beam

thinAlfoil I callimaiorTi_r

AS3-detectoi

pream.

amplifier MCA

Fig [3-13] The APM technique for deuterium accumulation in variousmaterials

60

collimators to stop the deuterons from entering to the (SB)

detector.

The sample was firmly held to a Cu sample holder. The

protons and tritons emitted according to the reaction (3.15)

were allowed to pass through two collimators to the SB

detector which was operated at a bias voltage of 60 volts.

The total charge received by the sample was measured using

the current integrator (C.I.)*

The number of implanted deuterons was assumed to be

proportional to the net count of protons emitted from the

reaction (3.15). i.e:

C a ND(3.16)

where C the net counts of protons and ND the number of

accumulated deuterons.

3-5-1 Calibration of the Current Integrator:-

To calibrate the current integrator C.I. the experimental

set-up in Fig[3-14] was used.

The background measured by the C.I. without any voltage

applied was found to be 25.16 counts per second. The readings

from the ammeter and the C.I. were taken by varying the

voltage of the power supply. The results of the readings

without neutron generator ammeter connected are shown in

Table [3-10]. The plotting of these data is shown in

61

+ sampleD-beam

ammeter

pvwer supply

NG ammeterr (/*)

Fig [3-14] Current integrator calibration set-up

62

Table [3-10]: Current versus C.I. count-rate with

neutron generator ammeter disconnected

ammeter (/iA)

25

50

75

100

125

150

175

200

CI (CPS-Bg)

23

48

70

94

129

141

164

188

63

Fig[3-15]. The slope of the straight line in Fig[3-15] was

0.93985, thus one count from the current integrator would be

equal to 1.064 micro Coulomb (nC) i.e:

1 count = 1.064 nC

The results of readings with the ammeter of the neutron

generator connected are shown in Table [3-11]. The graph

obtained from these data is shown in Fig[3-16].

The slope of the straight line obtained was 0.7052. Thus

one count from the current integrator was found to be equal

1.418 /iC i.e:

1 count = 1.418 JUC

This was the value used in these measurements.

The current integrator was operated with ±12 volt.

During the accumulation of the deuterium measurements the

high voltage of the neutron generator was set at 100 KV and

the target current was 50 /iA as obtained from the neutron

generator ammeter. The irradiation time was 2 hours. The

measurements were taken during the bombardment of the samples

by the deuteron beam. During the first 15 min the proton peak

net area from the MCA and the current from the current

integrator were taken every 1 min. After 15 min the readings

64

200 i ,

150

100

50

0C31-0 200 250100

ammeterFig[3—15] C.I. CPS versus ammeter readings with neutron

generator ammeter disconnected.

Table [3-11]: Current versus C.I. count-rate with

neutron generator ammeter connected

ammeter(MA)

25

50

75

100

150

200

C.I.CPS-Bg

19

35

53

71

106

140

N.G. ammeter(MA)

5

10

15

20

30

40

66

150

100

50 -

o•

—

C.I

N G ammeter

fitting

50 150 200100

ammeter

Fig[3-16] C.I. CPS versus ammeter readings with neutrongenerator ammeter connected.

250

were taken every 5 min.

The ion dose was calculated using the equation :

ion dose = [C.I.-(25.16X60 X period)] X 1.418 /iC (3.17}

where C.I. is the current integrator counts and the period is

one or five min.

The accumulation of deuterium was measured for the

materials: Cu, Au, Al, W, Pd, B, Zn, Co, Cd, metallic glass

(CuZr), steel, graphite (C), Ceramic, Si and Ni. The results

are shown in Tables from [3-12] to [3-26], respectively. The

summary of these results is shown in Table [3-27].

By plotting the results in tables from [3-12] to [3-26]

in semi-log paper the graphs shown in the figures from [3-17]

to [3-20] were obtained. A typical spectrum for these

measurements obtained on the MCA is shown in Fig[3-21], with

the tritium and proton peaks clearly indicated. Initially

some noise was observed in the spectrum that blurred the T

peak. The noise was traced to pickup from the radio-frequncy

oscillator of the neutron generator. It was removed by

Covering the APM head and preamplifier with Al foil.

From the results obtained it was found that Cobalt

showed the largest accumulation, while the metallic glass and

high TC ceramic showed the lowest accumulation. The

accumulations in Co, Zn, W and Al are shown in Fig[3-19],

while the accumulations in graphite, Au, B (amorphous), HTC

68

ceramic and metallic glass (CuZr) are shown in Fig[3-20].

The dependence of proton yield as a function of ion dose

indicates that the samples can be divided into three groups

from the point of view of self-target build-up, namely,

polycrystalline metals and semiconductors, with highest

accumulation, amorphous boron, with medium accumulation, high

TC ceramic and CuZr metallic glass with lowest accumulation,

as shown clearly in Fig[3-20].

These results show that the self-target neutron

background can be decreased by a factor of 100 if the target

material is selected properly. Further work is needed in this

field to investigate the effect of temperature on the

diffusion of deterium in the varius materials [12].

69

Table [3-12]: Accumulation results of Cu sample

N(net area)

28163144658912617222127835143650558767074884491899910781155125213491427149115821672176418392746352142905040571163687185786085309056

C.I.(mC)

1.4112.6804.2335.6587.3068.89210.31711.78513.33814.96116.30217.99619.40721.03123.39224.13725.69027.31428.86730.34932.39833.42634.93636.56038.15639.73741.29042.77244.39646.02061.62076.44090.905105.371119.411134.798149.477163.871178.408193.228

N(net area)

95509980104681100211542120741258513082135791405814524

C.I.(mC)

208.757223.435239.106253.217268.037282.716297.110311.788326.467340.578354.618

70

Table [3-13]: Accumulation results of Au sample

N(net area)

11214259811011211401652012252663043363714114514865245636066354747097547978298749149511393186123282742316836844313483653545984

C.I.(mC)

1.4532.8934.2905.8577.1268.67910.30311.92613.40814.89016.37217.99619.69121.10222.58424.20825.69027.31428.79630.42031.90233.38434.86636.48937.97139.31240.79442.27643.75845.24060.20274.88090.125105.087119.624134.586152.653165.147180.818196.135

N(net area)

66327298811189319799107421176212834139591506416292

C.I.(mC)

211.152226.484242.013257.117272.433287.608302.428317.390332.493347.313362.133

71

Table [3-14]: Accumulation results of Al sample

N(net area)

6194979108159197229274333396438507575642710795879953102011161207130214051517161017031807190219852965381046065390612769277648839190969755

C.I.(ittC)

1.3312.9034.4615.9487.3648.85110.33811.74113.10014.80016.21617.63219.04920.66322.00923.58125.06826.55527.97129.58631.08731.49534.20335.76137.17838.79240.15241.49742.98444.45759.57069.39389.440104.524119.679134.975150.541165.923180.227195.595

N(net area)

1039911029117101236513019137111440515126158451661317345

C.I.(mC)

211.033226.401241.343256.498271.369285.957300.970315.699330.571345.442359.888

72

Table [3-15]: Accumulation results of W sample

N(net area)

15633555578710531312159218132136250028263113352339704440660090601187415400188752299127286317393647641317464805153057000627806879075000813578783094440101157108097

C.I.(mC)

3.8147.06210.16813.27416.52119.76922.87525.69728.80331.90935.01438.12041.08444.19047.15462.25876.93691.611107.569122.531138.344153.306168.268183.371197.482211.452226.697241.659256.904272.575287.679302.641317.319331.572345.967360.645

73

Table [3-16]: Accumulation results of Pd sample

N(net area)

1623385274911071281451782092282582903163363613904244474725035315615936236486736987341133155520432565317638754508525060226804

C.I.(mC)

1.4822.8934.3755.9137.3818.82110.23211.92613.33814.89016.30217.92519.40721.10222.58423.78325.26526.88828.37029.85231.26332.67534.22735.63937.12138.60340.08541.56743.04944.53159.84775.16390.054105.016119.695134.302148.980163.588178.408192.944

N(net area)

7664854595551058611611126871376814770158371699118077

C.I.(mC)

207.339221.521236.341251.374266.407281.368295.834310.158324.411338.664353.129

74

Table [3-17]: Accumulation results of B sample

N(net area)

517263246557078102115128141149165193301377469553632726823905989106911471211125013331405

C.I.(mC)

2.5315.3608.55111.64314.79117.89720.67723.78327.10130.17933.18536.40439.69542.98546.37462.24478.32693.812109.753125.580141.024156.142171.600187.058202.530217.932233.362278.673294.131309.873

75

Table [3-18]: Accumulation results of Zn sample

N(net area)

1002294176298821135146517622133245528103210360339734382641984881059712718148341684518859206162237524140257882737328842302333137632324334313465835786

C.I.(mC)

3.8147.48711.30214.55017.93921.18724.43427.68230.93034.03637.28340.35143.77847.02650.13266.51282.89299.130115.085131.039147.135162.948178.477193.864209.961225.915241.444256.548272.644288.032300.725315.970331.641347.028

76

Table [3-19]: Accumulation results of Co sample

N(net area)

13329550575310281345168220662465284932453647407845695115807311590154251964324365294353481040364462545223558339645747108477553845459151598422105682113310121250128750

C.I.(mC)

3.3046.6229.88413.13216.66320.47823.72526.97330.36333.72537.00040.24743.63747.02650.41567.78886.011102.817120.331136.711153.800170.889187.127203.365219.603235.841252.079267.608282.996299.234315.188331.001347.948364.895381.700367.513

77

Table [3-20]: Accumulation results of Cd sample

N(net area)

16701532513825366888389821149132015101690189120753074425156547078872510351119701386415724176721958421614235522555527535296983173133749358923797640180

C.I.(mC)

3.3896.4959.53012.56515.52918.49321.45724.42127.24330.20733.17136.13539.95741.92145.02759.56374.10088.495103.173117.143130.970145.365160.752175.430190.109204.645219.040233.718248.538263.500278.462293.566308.386323.773339.019354.406

78

Table [3-21]: Accumulation results of metallic glass (CuZr)sample

N(net area)

1234444478910111314141616171820222324242628282929395165738296111119129140

C.I.(mC)

1.3122.7204.0755.4406.7748.1619.52610.91312.45914.11215.91417.57719.40021.19123.01424.76326.11428.21830.07231.84233.61235.43537.04539.01740.80842.71744.47646.24648.04749.68967.86785.565103.119120.961138.872156.251175.014193.744212.230230.449

N(net area)

154162178191203214226236250272292

C.I.(mC)

248.360266.378284.395302.093319.579337.277354.975372.886390.585408.399426.088

79

Table [3-22]: Accumulation results of steel sample

N(net area)

101831455983101125150172196231256285321517790110214261803222826603174371042514746527458706365698275708189882294741009410776

C.I.(mC)

2.5385.0777.75710.72113.68516.93320.03923.28626.25029.49832.88736.27739.80843.26846.58763.39278.90795.301111.681127.636142.456157.843173.372188.760204.572219.534235.489251.160266.689282.076297.321312.567327.103342.916359.154375.250

80

Table [3-23]: Accumulation results of graphite (C) sample

N(net area)

102844669914418624029934941045451259066573283891210061086114012481399150616161732184719542076218834794635578469448088924610415113851240513450

C.I.(mC)

1.4162.9744.6036.3037.7909.34810.90612.53514.02215.65117.13818.62520.11221.59923.08624.57326.06127.68929.17730.66432.29333.85135.48037.10938.80840.43742.06643.69545.18246.66962.95978.53993.410108.707124.287140.435155.519170.177185.020199.778

N(net area)

1441515450163811745018404193222041521520224672342924308

C.I.(mC)

214.961229.535243.796258.738273.567288.141303.749318.748333.307347.679362.072

81

Table [3-24]: Accumulation results of HTC ceramicsample

N(net area)

1617192225283135363843485555577791103114126134144164173186195207217227242252260267276282297

C.I.(me)

3.3186.6089.99813.24516.59219.84023.15826.54829.86633.18536.36139.75143.14046.31749.56566.01582.75099.697116.857134.159151.248167.627184.291200.813217.193233.998250.732267.608284.697301.928318.932335.822351.677367.377382.934398.591

82

Table [3-25]: Accumulation results of Si sample

N(net area)

0351215314058891211631912262662913403864364775205746436837387918438959591016107117902571344943115164604567877707873110102

C.I.(mC)

0.9932.0393.0434.1855.4336.8098.1229.59411.05512.59114.11615.69417.16618.74420.11021.62423.05324.41925.78527.04428.40929.77531.03432.37833.65834.91736.17737.43638.80139.98653.92868.00982.56896.542110.730124.917138.987153.929169.446186.336

N(net area)

1149112888143891590517352187452014421494228742412025322

C.I.(mC)

202.981219.498235.877252.075268.262284.333300.201316.058331.746347.316362.780

83

Table [3-26]: Accumulation results of Ni sample

N(net area)

33132295494761101213321684204024512820324336304023447653437456958511589133031493016464181101947121025224082388324816

C.I.(mC)

2.7155.7158.89212.35215.60018.98922.37825.91029.17532.68835.93639.32542.43145.67948.92766.15782.04198.066113.738128.203143.732158.623173.301187.483202.658215.706230.029240.595

84

Table [3-27]: Summary of deuterium accumulation indifferent materials

element

Cu

Al

Au

Pd

Si

graphite C(amorphous)

Ni

Zn

Co

W

Cd

CuZr

B(amorphous)

Steel

Ceramic

proton areaafter 2 hrs

14524

17345

16292

18077

25322

24308

24816 (80 min)

35786

113310

108097

40180

292

1405 (90 min)

10776

297

ion dosein mC

354.618

359.888

362.133

353.129

362.780

362.072

240.595

347.020

367.513

360.000

354.406

426.088

309.000

375.250

398.591

85

icr

6

'Ia,

10

1CT

10'

10

"T"

-1 00

o

0 300100 200ion dose (mC)

Fig [3-17] Accumulation comparison of Cu, Pd and steel

400

C

IoG

10

5

4

2

1

0

-

©ooI

I I

C^i^oOO

i i

£&'

o

n•

-

-

Si

Ni

Cd

_10 -

10

- 1 00 0 300100 200ion dose (mC)

Fig [3-18] Accumulation comparison of Si, Ni and Cd

400

M

0-I-J

oU

a,

14

12

10

4

2 J

-100 0

•

o

•

V

Al

Zn

Co

W

400100 200 300ion dose (me)

Fig[3 — 19] Accumulation comparison of Co, W, Zn and Al

500

12

10

8

4 -

0

2 i i

-100 0

I I I I

. . . • % % # o # o o " ° O # O # S S 8

'°°°• •

i i i

V HTc

0 Au• c

• B

• Cu-Zr

i

-

400 500100 200 300

ion dose (mC)

Fig [3-20] Accumulation Comparison of C,Au,B,HTc and Cu-Zr

TAG NO. - 3 1 SERIES 3 5 + V - 2 . 1 0UH# 0 MEMORY « i / 2 VFS =

15: 10 10 FES 1992IK CH# 1023

CANBERRA

i i!

-.!_=• CH# 377OUNTS i

i j 1

U..1FROM CH# 364 70 CH# 482 PSET (L) 100000

ELAP (L) 7885

Fig[3-21]: Typical spectrum of Zn sample where the tritium peak and the proton

peak are indicated.

3-6 Gamma-Ray Spectrometer System:-

Gamma ray spectrometry is used for the identification

and quantification of radionuclides present in a sample using

the emitted gamma radiation.

The measurement of gamma radiation emitting from sample

•results in a pulse height distribution or gamma-ray spectrum.j1

In this distribution, the pulse height is proportional to the

! gamma-ray energy and the height of each point in the

.distribution is proportional to the intensity. The shape of

the pulse height distribution is determined by the response

function of the spectrometer.

Gamma radiation is measured with a gamma-ray

spectrometer compising a gamma-ray detector, electronics for

analog processing of the signals produced by the detector and

a multi-channel analyzer for digitizing the signals and

spectrum accumulation [13].

3-6-1 Interaction of Gamma-Rays with Matter:-

Gamma rays are electromagnetic radiation of very small

(10 to 10 cm) wavelength. Gamma-rays are emitted by the

nucleus when it makes a transition from a higher energy

excited state to a lower energy state in radioactive decay

[14].

There are three important processes by which gamma-rays

interact with matter and lose their energy. These are: the

photoelectric effect, the Compton effect and pair

production [15].

91

3-6-2 Radiation Detectors:-

Scintillation and semi-conductor detectors are commonly

used for gamma-ray measurements. The scintillation detector

(e.g. Nal-detector) has a good detection efficiency but one

of its major limitations is the poor energy resolution. The

chain of events which must take place in converting the

incident radiation energy to light and the subsequent

generation of an electrical signals involves many inefficient

steps. Therefore, the energy required to produce one

information carrier (photoelectron) is of the order of 1000

eV or more, and the number of carriers created in a typical

radiation interaction is usually not more than a few

thousand. The semiconductor detector (e.g. Ge-detector), has

the advantage of a good energy rsolution, because the number

of information carriers (electron-hole pair) per pulse is

very large. In a Ge-detector the energy needed to create

electron-hole pair is about 2.97 eV. Thus using a Ge-detector

results in a much larger numbers of carriers for a given

incident radiation event than is possible with a

[scintillation detector [16]. •

The Ge-detector, however, has to be cooled with liquid

jitrogen to limit excessive noise.

-6-3 The Counting System:-

The signals from the detector are processed by a

jjeamlifier where the extremely small charge pulses from the

92

detector are converted into voltage pulses of several mV.

These signals are further amplified and shaped in the main

amplifier to signals which can be fed into an analog-to-

digital converter [13].

A detector can be represented as a capacitor into which

a charge is deposited, as shown in Fig[3-22], During the

charge collection a small current flows, and the voltage drop

across the bias resistor R yields the pulse voltage [17].

The preamplifier is isolated from the high voltage by

the capacitor C. The rise time of the pulse is related to the

collection time of the charge, while the decay time of the

pulse is related to the RC-time constant characteristic of

the preamplifier itself.

The primary purpose of the preamplifier in a nuclear

counting system is to optimize the coupling of the detector

output to the rest of the system. The preamplifier is also

required to minimize any source of noise which may degarde

the resolution of the spectrum [17].

The amplifier serves to shape the pulse as well as its

further amplification. The long decay time of the preamlifier

pulse may not be returned to zero voltage before another

pulse occurs, so it is important to shorten it. The RC-

clipping technique can be used, in which the pulse is

93

pieamp amp to PHA

Fig[3-22] Detector and counting system schematic

94

differentiated to remove the slowly varying decay time, and

then integrated somewhat to reduce the noise. The unipolar

pulse output that results is much shorter [17].

A near gaussian pulse shape is produced, yielding

optimum signal-to-noise characteristics and count-rate

performance.

3-6-4 The Multichannel Analyser (MCA):-

The MCA consists basically of an analog-to-digital

converter (ADC), a memory and a display oscilloscope. The MCA

collects pulse in all voltage ranges at once, providing a

major improvement over single channel analyser spectrum

'analysis. An input pulse is first checked to see if it is

within the selected MCA range, and then passed to the ADC.

•The ADC converts the pulse height to a number proportional to

the pulse voltage. This number is taken to be the address of

a memory location. After collecting data for some period of

stime the memory will contain a list of numbers correspondings

!to the number of pulses in each voltage limit.

The display shows a point plot of memory contents versus

[channel number i.e. a spectrum [17].

The MCA also provide some basic facilities for

^Calculations of the spectral data, e.g. peak area integration

land background subtraction. Computer processing of the

[measured spectra reguires interfacing of the MCA with a

fcomputer [13].

95

J-6-5 Effeciency Measurement:-

To relate the detected number of pulses to the source

activity it is necessary to have a precise value for the

ietector efficiency.

It is convenient to subdivide counting efficiencies into

two classes: absolute and intrinsic. Absolute efficiency is

iefined as:

no. of pulses recorded:abs

no. of radiation quanta emitted by source(3.18)

ind is dependent not only on detector properties but also on

the details of the counting geometry (primarily the distance

from the source to the detector). The interinsic efficiency

Ls defined as:

no. of pulses recorded:int no. of quanta incident on the detector

(3.19)

[he two efficiencies are related for isotropic sources by:

€int = eabs X(3.20)

fhere ft is the solid angle subtended by the detector at the

source position. The intrinsic efficiency of a detector

usually depends primarily on the detector material, the

radiation energy and the physical shape of the detector [16].

96

Counting efficiencies are also classified as total or

photo-peak efficiencies. For total efficiency the entire area

under the spectrum is a measure of the number of all pulses

recorded regardless of amplitude. The full-energy peak

efficiency assumes that only those interactions which deposit

the full energy of the incident radiation are counted. The

number of full energy events can be obtained by simply

integrating the total area under the peak, which is shown as

the cross-hatched area in Fig[3-23].

It is often preferable from an experimental point of

view to use only full-energy peak efficiencies, because the

number of full-energy events is not sensitive to some

perturbing effects such as scattering from surrounding

'objects. Therefore, values for the full-energy peaki

[efficiency can be measured using standard sources, and

(applied to a wide variety of cases [16].

The efficiency measurement of the HPGe detector at the

jHeutron Generator Laboratory, University of Khartoum, was

^done using standard sources from the IAEA. A block diagram of»

jthe gamma-ray spectroscopy system used for the measurement is

shown in Fig[3-24].

The net area under the peak from any gamma-ray line E of

a standard gamma-ray source may be described by the following

relation:

NC(E) = I (E) e K (3.21)

97

dN/dH

-» H

Fig[3-23] Integration of the total area under the full-peak energy

98

MCA \

H.V

+2000 V

s HPGedetector

gammasource

pulser

Fig[3-24] A block diagram of gamma-ray spectroscopy system

99

where I (E) is the intensity of the gamma line, e the

photopeak efficiency of the line and A is the activity of

the calibrated source.

The activity of the source A is related to the activity

at the time of calibration A» as:

= AQ exp(-rt) (3.22)

where t is the elapsed time from the date of calibration and

r is the decay constant.

Thus the photopeak efficiency, e , will be given by the

relation:

NC(E) NC(E)

IT(E) iT(E) A 0 t](3.23)

where ti is the half-life of the source.

Because of the dead-time effect not all pulses belonging

to the full-energy peak will be detected in it. The

correction for such losses was done using a pulser. The

pulser has an output frequency of 50 Hz. It was connected to

the preamplifier of the detector as shown in Fig[3-24]. The

relation for obtaining a corrected count is given by:

5 0 (3.24)

100

where Nt r u e

(E) * s t n e n e t a r e a after correction, NC(E) the

net area before correction, T the true counting time and N

the pulser peak area.

The cascade process will remove events which would

otherwise fall within individual gamma-ray full-energy peak.

Thus a correction for cascade losses is needed for sources

measured at small distances to the detector. To solve this

problem efficiency ratio measurements were done.

3-6-6 Efficiency Ratio Measurements:-

The distances used at laboratory for which cascade

correction was needed were 0 and 1.2 cm. By measuring the

i[efficiency for these cases and taking the ratio of the valuesi^Obtained for the same isotopes at 0 and 1.2 cm distances to

Ithose obtained at 15 cm distance it is possible to

|Prenormalize" the efficiency curves to 0 and 1.2 cm

Jistances.

To perform such measurements an Al-foil of thickness 0.1

was used. The foil was irradiated by fast neutrons using

le neutron generator. The count from the Al-foil was first

jollected at a 15 cm distance from the detector. The foil was

len collected at 0 and 1.2 cm distances from the detector,

le waiting times T between each counting of the foil were

;aken into account. Then the efficiency ratio was calculated

is follows:

101

1,0Al,0 P15

15P exp(-r tw)

(3.25)

where A is the area of the peak at 1.2 or 0 cm distance,11 u

A 1 5 the area of the full peak at 15 cm distance, P1 Q and P 1 5

are the areas of the of the pulser peaks at 1.2 ,0 cm and 15

cm, respectively, T the decay constant of the gamma line and

t the waiting time.

The nuclear reaction used was :

27Al(n,p)27Mg (3.26)

27The product nucleus Mg has a half-life of 9.45 min and it

gives two gamma lines of energies 844 KeV and 1015 KeV with

intensities 72% and 28%, respectively [8],

The results of the efficiency ratios are given in Table

[3-28].

The photopeak efficiencies ratios were plotted versus

the gamma-ray energies. The result of the efficiency ratio of

1.2 cm to 15 cm is shown in Fig[3-25]. The result of the

efficiency ratio of 0 cm to 15 cm is shown in Fig[3-26]. The

| comparison between the two measurements is shown in

I Fig[3-27]. These graphs show that the efficiency ratio is not

II' constant with energy.

The obtained data were fitted using the following

102

Table [3-28]: Efficiency ratio results for 0 and 1.2 cmdistances to 15 cm distance.

source

241Am

109Cd

57Co

137Cs

54Mn

27A1

22Na

ET [KeV]

59.537

88

122.060136.474

661.660

834.843

8441015

1274.542

Ve15

31.743

33.034

45.30047.500

42.007

40.881

40.62538.600

35.880

el.2/el5

27.336

24.810

32.70031.900

28.653

27.653

27.71825.900

24.408

103

35 r

25

20

o measured

fitted

0 200 4 001

1200600 800 1000gamma energy (KeV)

l''ig[3 -25) Efficiency ratio of 1.2 to 15 cm distances vervusgamma energy for the HPGe detector

1400

50

45

40

35

30

2 s0 200

Q measured

— fitted

_L

1200400 600 800 1000gamma energy (KeV)

Fig[3-26] Efficiency ratio of 0 to 15 cm distances versusgamma energy for ttie HPGe detector

1400

a 1 l.o 15 cm

400 600 800 1000 1200 1400gamma energy (KeV)

i[3~27] Comparison of the efficiency ratios 0 and 1.2

to 15 cm dislances of the HPGe detector

jxperimental formula [ 1 8 ] :

R == a., exp(-a2 E)+a_ exp(-a4 E)+a5 exp(-a, E) ( 3 . 2 7 )

jjhere R is the efficiency ratio and E is the energy of the

lamina line in KeV. The values of the parameters a.. , ao, a_,

f., a5 and a6 are shown in Table [3-29].

$-6-7 Efficiency Measurement of the HPGe Detector at 15 cm

Distance:-

The calibrated sources from the IAEA were measured at a

distance of 15 cm from the detector, with the correction for

le dead time, then the photopeak efficiencies of the gamma-

ly lines were calculated using equation (3.23). The results

ptained are shown in Table [3-30].

|?-6-8 Photopeak Efficiencies Measurement of the HPGe Detector

at 0 and 1.2 cm:-

The photopeak efficiencies at 15 cm were then used to

jind the photopeak efficiencies at 0 cm and 1.2 cm. This was

jne using the photopeak efficiency ratios (eo/ei5^ anc*

•- /e.K) at a certain energy line, using equation (3.27)

id the parameters of Table [3-29]. The photopeak efficiency

ratio (eQ/e15) and (e ^ 2/ei5^ f o r a certain line were

|ultiplied by the photopeak efficiency for the same line at

cm from Table [3-30]. In this way the corrected photopeak

107

Table [3-29]: Parameter values fitted to the efficiencyratios of 0 and 1.2 cm distances to 15 cmdistance.

parameter

al

a2

a3

a4

a5

a6

for eo/e15

54.9999

0.00035

-61.03542

0.01569

-48344.733

2.57529

f o r ei.2/£15

28.5027

0.00013

-50.7704

0.00662

39.0060

0.00351

108

Table [3-30]: Results of the photopeak efficiencies of the HPGe detector at 15 cm distance usingthe IAEA calibrated sources

source

57CO

22Na

137Cs

54Hn

109Cd

133Ba

60Co

52EU

activityKBq

34.669

41.403

41.847

41.366

39.590

38.184

33.226

34.003

386.5

tdays

1.5X105

271.77

950

11009

312.5

462.6

3890.9

1925.2

4931

E.KeV

59.537

122.063136.276

1274.450

661.645

834.827

88

80.997276.399302.851356.005383.851

1173.2381332.501

121.779244.693344.272778.890964.050867.3801112.081408.03411.111443.979

{

36

85.5910.58

99.84

84.60

99.98

3.72

347.118.3362.308.92

99.8799.98

28.377.5126.5812.%14.624.1613.5620.582.2343.121

t

s§c

1000

1500

1000

1000

1000

2000

1000

1000

1000

-

i... *

tHdays

1893

1893

1886

1886

1886

1889

1922

1922

2840

area ofpeak

9246

1804212

5084

26957

510

611

1726635958160234473141

86587649

2223904355910948323460214886864178532189176269933

pulser 'area

49803

74606

49874

49294

49824

99953

49900

49860

48420

photopeakefficiency £-5

0.00075626

0.004259330.00404930

0.00048220

0.00087980

0.00085070

0.00364550

0.002156620.002150300.001890550.001598310.00149542

0.000510680.00045067

0.003121700.002309800.001640320.000720900.000585300.000657100.000524300.000423600.001359400.00126740

\oc\

Jficiencies at the distances 0 cm and 1.2 cm from the

;ector were calculated. The results of the photopeak

Jficiencies of the HPGe detector at 0 cm, 1.2 cm and 15 cm

Stances are shown in Table [3-31].

The fitting of these data were done by dividing the

nas energies into two regions: 50 to 250 KeV region and

to 2500 KeV region. The fitting was performed using the

[ation [18] :

2 3e = a +a2 lnE +a3 In E +a4 In E (3.28)

:e e is the efficiency and E is the energy of the gamma-

line in KeV. The values of the parameters a ^ a2, a3 and

for the energy region 50 to 250 KeV are shown in Table

r32]. The parameter values for the energy region 250 to

}0 KeV are shown in Table [3-33].

The comparison of the measured effeciency and calculated

tciency using equation (3.28) and parameters of Tables

l\ and 1^-3Vi for Xke energies 50 xx> 250 ¥.e\ for tr*s

jtances 0 cm, 1.2 cm and 15 cm are shown in Figs. [3-28],

J-29] and [3-30], respectively. The comparison between

3asured and calculated efficiencies for the energies 250 to

8500 KeV, for the distances 0 cm, 1.2 cm and 15 cm are shown

Figs. [3-31], [3-32] and [3-33], respectively.

The results show that the measured and calculated

[efficiencies are in good agreement.

110

Table [3-31]: Photopeak efficiencies of the HPGe detector atdistances 0 cm, 1.2 cm and 15 cm.

source

1 3 7Cs

54Mn

22Na

104Cd

241Am

57CO

133Ba

60Co

152Eu

E KeVT

661.645

834.827

1274.54

88

59.537

122.063136.476

80.997276.397302.851356.005383.851

1173.2381332.501

121.779244.693344.272411.111443.979778.890867.380964.0501112.081408.03

£15

0.0008798

0.0008507

0.0004822

0.0036455

0.0007563

0.00425930.0040493

0.00215660.00215030.00189060.00159830.0014954

0.00051080.0004507

0.00031220.00230980.00164030.00135940.00126740.00072090.00065710.00058530.00052430.0004236

£1.2

0.025210

0.023524

0.011767

0.090461

0.020673

0.1359600.135992

0.0600810.0733990.0643510.0536780.049730

0.0128100.010962

0.0962160.0787320.0552910.0447160.0411000.0201840.0178450.0154420.0133280.010170

eo

0.037020

0.034778

0.015519

0.120427

0.024006

0.1929430.192607

0.0783900.1056500.0925300.0772400.071690

0.0186300.015550

0.1363700.1135900.0795300.0646200.0596000.0301900.0266800.0229700.0195400.014230

111

Table [3-32]: Parameter values for energies 50 to250 KeV

parameter

al

a2

a3

a4

at distance0 cm

19.22546

-13.39557

3.065720

-0.229450

at distance1.2 cm

10.98131

-7.786510

1.809010

-0.137040

at distance15 cm

-0.03232

-0.00542

0.00669

-0.00083

112

Table [3-33]: Parameter values for energies 250 to2500 KeV

parameter

al

a2

a3

a4

at distance0 cm

5.931500

-2.476880

0.349990

-0.016680

at distance1.2 cm

3.13530

-1.566210

0.217440

-0.010180

at distance15 cm

0.12588

-0.05323

0.00762

-0.00037

113

0.3

0.2

o

0>

0.

fitted

measured

0.0 '50 00 250150 200

gamma energy (KeV)

Fig[3-28] The HPGe detector Efficiency at 0 cm for the

energy range 0 to 250 KeV

300

0.2

0.1

_ir\ C) I ___ _J L

50 100 150 200gamma energy (KeV)

Fig[3-29] The HPGe detec tor efficiency a t 1.2energy range 0 to 250 KeV

250 300

cm for the

0.005

0.004

.0.003

0.002

0.00

measured

fitted

0.00050 100 250150 200

gamma energy (KeV)

Fig[3-30] The HPGe detector Efficiency at 15 cm for theenergy range 0 to 250 KeV

300

0.15 1

measured

fitted

0.10

0.05

0.00 _L

200 400 200 1400600 800 1000gamma energy (KeV)

Fig[3-31] The HPGe detector efficiency at 0 cm for theenergy range 250 to 2500 KeV .

1600

0.08

0.0/

0.06

0.05

g 0.04u

"S 0.05

0.02

0.01

0.00200

' . » •

measured

r - fitted

._ ,._..l 1 J L J L_ _ J

400 600 800 1000 1200 1400 1600gamma energy (KeV)

Fig [3 32] The HPGe deleeLor efficiency at 1.2 cm for theenergy range 250 to 2500 KeV

0.003

0.002

o

o

0.001

measured

_ fitted

0.000 L -200 400 400 1 600600 800 1000 1200

gamma energy (KeV)

Fig[3-33] The HPGe detector efficiency at 15 cm for theenergy range 250 to 2500 KeV

3-6-9 "Total-to-Peak11 Efficiency Ratio Measurement :-

The total and full-energy-peak efficiencies are related

by the "total-to-peak11 ratio r:

r = etotal/epeak <3'29>

The "total-to-peak11 ratio was measured using the

relation:

r = eT/ep = NT(E)/NC(E) (3.30)

where NT(E) is the total count from the beginning of the

spectrum upto the end of the peak of energy E and NC(E) is

the net area under the peak of energy E.

The ratio in equation (3.30) was found for various

points using some of the standard gamma-ray sources of the

IAEA and Al-foil after irradiation by neutrons from the

neutron generator. The results are shown in Table [3-34].

These data were fitted using the logarethmic formula:

r = a^ +a2 lnE +a3 ln2E +a4 ln

3E (3.31)

where r is the "total-to-peak" ratio and E is the energy of

the gamma line in KeV. The parameter values are a = -164.4164

a2= 102.84288, a3= -21.0599 and a4= 1.42309.

The comparison between the measured "total-to-peak"

120

ratio and calculated using equation (3.31) is shown in Fig[3-

34]. The result shows the clear increase of efficiency ratio

£ TA P with energy.

121

Table [3-34]: Results of total-to-peak efficiency ratio

source

241Am

57CO

109Cd

137CS

60CO

27A1

Er KeV

59.537

122.063

88

661.645

1173.238

844

peak area

246685

35238

6771

374776

110069

2164

totalintegration

325788

56017

13824

1686510

1392583

18314

r= NT/NC

1.320664

1.589676

2.041650

4.500050

12.65191

8.463000

122

CO

oc

ID

OH

E -

14

10

2 -

0

fitted

A measured

0 200 400 600 800 1000 1200gamma energy (KeV)

1400

Fig[3-34] Total-to-peak efficiency ratio for the HPGe detector

REFERENCES

1- "Neutron Sources for Basic Physics and Applications" p(32-

50), CIERJA CKS, Ed. Pergman Press, Oxford (C.A. Uttly).

1983.

2- A. Grallert, J. Csikai, S.M. Qaim and J. Knieper:

Recommended Target Materials for D-D Neutron Sources. 1992

(to be published).

3- G. Paic, Rudjer Boskovic Institute, Zagrib, Yugoslavia,

Production and Current Uses of 14-MeV Neutrons, paper

presented at Second Winter Nile College, Department of

Physics, University of Khartoum (1987).

4- "Texas Nuclear Corporation Neutron Generators", J.T.

Prudhomme, Texas Nuclear Corporation, Austin, Texas

(1962).

5- M. Drosg, Sources of Variable Energy Monoenergetic

Neutrons for Fusion Related Applications. Nuclear Science

and Engineering, 106, 279-295 (1990).

[6- "HandBook of Fast Neutron Generators" Volume 1, J. Csikai,

CRC Press, 1987.

|7- J. Csikai, Accelerator Based Prompt-Gamma Analysis, IAEA-

AGM on Low Energy Accelerators in Elemental Analysis,

Chiang Mai, Thailand, 25-29 March 1991.

I- "Table of Isotopes" Ed. by G. Michael and Virginia S.

Shirly, 7-th edition, Wiley Interscience Publication

(1989) .

124

9- J. Csikai, The Properties of D-D and D-T Neutron Sources,

IAEA Interregional Training Course on Neutron Generators,

Leningrad, 25 Sept-29 Oct 1989.

10- J. Csikai, Cs. M. Buczko, R. Pepelnik and H. M. Agrawal,

INDC(NDS)-232/L, IAEA Vienna, p61. (1990).

11- J. Roth, R. Behrisch, W. Moller, and W. Ottenberger,

Fusion Reactions During Low Energy Deuterium Implantation

Into Titanium, Nuclear Fusion, Vol. 30, No. 3 (1990).

12- A. Grallert, J. Csikar, S. M. Qaim, G. Stocklin, J.

Knieper, N. I. Molla, M. M. Rahman, R. Miach, I. Shaddad

and F. Habbani: Recommended Target Materials For D-D

Neutron Sources, 16-th World Conference In Legnaro

(Italy), 21-25 Sept. 1992.

13- M. de Bruin: High Resolution Gamma-Ray Spectroscopy, IRI-

Report 133-86-37 (1987)

14- "Nuclei and Particles" By: Port Emito Segre and W. A.

Benjamin, New Yourk (1969)

15- "Introduction To Experimental Nuclear Physics" By: R. M.

Singru, 1974.

16- "Radiation Detection and Measurement" second edition By:

Glenn E. Knoll, University of Michigan, 1989.

17- Canberra Industries, Inc-Meriden, 1981-1982.

18- F. Cserpak and J. Csikai, Institute of Experimental

Physics, Debrecen, (private communication).

125

CHAPTER FOUR

CORRECTIONS USED IN CROSS-SECTION MEASUREMENTS

In cross-section measurements a number of corrections

are needed for doing precise measurements with good accuracy.

These corrections could be divided into two groups: one

which is related to the irradiation circumstances like the

background neutrons which contaminate the neutron spectra due

to the scattering from walls, the variation of neutron flux

with time, the decrease of the neutron flux in space and the

attenuation of neutrons in samples. The other group is

related to the counting geometry like the cascade

| corrections, dead-time corrections and self-absorption

corrections.

All those factors are affecting the activity of the

irradiated samples specially in using the relative method for

the cross-section measurement.

In this chapter the methods used in doing these

corrections are discussed.

4-1 Scattered Neutrons:-

The neutrons which are scattered from the walls or

surrounding materials near the TiT target will contaminate

the neutron flux and this will affect the monochrontaticity of

126

I

the neutron flux. In solving this problem the irradiations

are done in scattering free arrangement. A special attachment

for holding the samples at a distance of about 10 cm away

from the target is usually used.

4-2 Attenuation of Neutrons in Samples:-

In the relative method of the cross-section measurement

the sample and the monitor are placed back-to-back, so that

neutrons will be removed from the flux by the first sample

due to scattering and absorption. Thus the flux of neutrons

which irradiate the back sample need to be corrected.

In order to calculate the correction of attenuation

produced by samples, it is convenient to use the "removal

cross-section" concept [1].

The correction factor e . of the neutron flux

attenuation in samples are calculated using the following

relation [2]:

at (4.1)

-1where 2 is the macroscopic removal cross-section in cm A and

x is the thickness of the attenuater in cm. Equation (4.1)

can also be written in the following form:

mat M

(4.2)

127

where a is the microscopic removal cross-section in cm of

the attenuater, N the Avogador's number, M is the atomic

weight of the attenuator, m is the mass of attenuator in gm

and A is the surface area of the attenuator.

4-3 Correction of The Flux Due to The Distance From The

Target:-

The flux of neutrons depends strongly on the distance

from the target i.e.

a 1/r' (4.3)

where * is the neutron flux and r is the distance between the

target and the sample. This effect is especially significant

at small distances [3].

In the relative method of cross-section measurement the

sample and the monitor are placed back-to-back. Thus, a

correction for the flux difference due to the distance

between the sample and the monitor may be done using the

relation (4.3).

4-4 Correction Due to The Variation of The Flux With Time:-

Using the neutron generator for activation it is

Impossible to guarantee the same neutron flux throughout the

jame irradiation. This variation may be caused by the fast

128

aging of the target, instability of the accelerating voltage

or fluctuations of the deuteron beam. The variation of

neutron flux with time results in the variation of activity

of the sample. Because of this the neutron flux must be

measured continuously during the irradiation. The monitor

used in the relative cross-section measurement serves as

neutron flux monitor [3]. from the general equation of the

neutron activation technique (3.1), the activity A is a

function of the decay constant r of the product nuclide and

of the flux *(t) i.e.

A a «(t) (l-exp(-rtirr)) (4.4)

where t. is the irradiation time. In the case of the

relative method of the cross-section measurement the sample

and the monitor will also be activated differently because

they have different half-lifes.

For the flux correction a long counter based on BF3 gas

may be used to measure the neutron fluence in equal intervals

9. We defined a quantity called the flux function S (at

constant flux with time) as:

S = #(l-exp(-rtirr)) (4.5)

flux function may also be written as:

129

S = S exp(-r(m-i)6)] (l-exp(-re)) (4.6)a

where i=l,2,...,m; m is the number of intervals, C. is the

neutron fluence measured by the neutron detector in the

interval 0, r is the decay constant and a is the monitor-to-

fluence rates conversion factor [4]. The relation (4.6) can

be used for the neutron flux correction.

4-5 Dead-time Correction:-

Because of the dead-time effect pulses belonging to the

full-energy peak will not be detected in full. Therefore a

correction should be done. This may be done using a pulser.

Suppose the pulser has an output frequency F Hz. It is

[connected to the preamplifier of the detector and the count

|for a given true time T will be observed in the MCA, where it

Is expected to find in the peak related to the pulser a

lumber of pulses FT. However, due to the dead-time effect the

rea under the pulser peak will be smaller. The fractional

^crease in the area of the pulser peak is equal to that of

ly of the full-energy peaks in the spectrum. In this way we

pan easily compute the true area A. from knowledge of the

measured area of a gamma peak A and the measured area under

le peak belonging to the pulser N :

130

At - A FT/N (4.7)

The correction factor of the dead-time, ed, of the peak

area A will then be:

= FT/N (4.8)

4-6 The Cascade Correction:-

Additional peaks caused by the coincident detection of

two (or more) gamma-ray photons may also appear in the

recorded pulses height spectrum. The most common situation

occurs in applications involving an isotope which emits

multiple cascade gamma-rays in its decay, as illustrated in

Fig[4-1]. Assuming that no isomeric states are involved, the

life-times of the intermediate states are generally so short

that the gamma-rays are, in effect, emitted in coincidence,

which can lead to summation effects in gamma spectra.

The correction factor e for true coincidence losses may

affect peaks within the same spectrum differently, depending

upon the gamma-ray cascade relationships and the total

detection efficiency of the detector for the coincident gamma

-energies. A gamma quantum (T) emitted before or after the

investigated one (T_) within a time interval less than 10

sec could cause coincidence losses. The e correction factor,

which is the probability of the detection of a given T 0

quantum without the detection of any other gamma quanta from

131

Fig[4-1] Gamma Cascades

132

its cascade, may be calculated by the following expression

[5]:

no

ec "5

7T1 (1- j ) T..

(4.9)

where nQ is the number of cascade chains containing the TQ

transition, n. is the number of cascade gamma transitions

(excluding T Q) in the i-th cascade chain (i=l,2,3...nQ), B^

is the branching ratio of the B~ (or B , EC, a) transition

populating the i-th cascade chain, T^. is the branching ratio

of the j-th gamma-transition in the i-th cascade chain, e. .

=(£4. e ) is the product of the total detection effeciency,

€¥, and the self-absorption, e . for the energy of the j-th

gamma-transition of the i-th cascade chain and S. =1 if the

i-th chain is initiated by B~, EC or a-decay; S. =(l-2e) if

the i-th chain is initiated by B decay where e =(£*. es) at

511 KeV.

4-7 The Self-Absorption Correction:-

The gamma-rays emitted from the radioactive nuclide

inside the sample are self-absorbed by the sample itself.

This self-absorption is due to the attenuation of gamma-

radiation through its different interactions with matter. The

133

number of gamma quanta that arrive to the detector is less

[than the real number of quanta emitted from the radioactive

[nuclide. Therefore the measured activity of the sample is

less than the real activity of the radionuclide. Thus the

correction due to self-absorption of gammas through the

sample is needed.

The absorption coefficient of the element of the gamma

line is dependent on the atomic number of the element and the

energy of the gamma line:

/i = ji(Z,E) (4.10)

where n is the self-absorption coefficient, Z is the atomic

number and E is the energy of the gamma line.

The self-absorption correction (e ) of a thin sample is

negligible for high gamma energies but its role can be very

important below about 300 KeV. There is a well-known formula

for the self-absorption correction in "good geometry"

(parallel beam):

(l-exp(-nd)) (4.11)

where yi is the absorption coefficient of the gamma-ray in

cm2/g and d is the thickness of the sample in g/cm2 [5]. In

the case of the "bad geometry", when the sample is measured

on the top of the detector, the passage of gamma-rays inside

134

the sample is greater than the case of "good geometry". This

shown in Fig[4-2]. In this case one can suppose that it can

be described by an exponential formula using the "effective

absorption coefficient" (n f f ) - This exponential formula is

given by:

eg = a exp(-/ieff d) (4.12)

where a is a constant.

Some measurements have been done to find the effective

self-absorption coefficient M e f f / for different gamma

energies in different elements.

To measure fi f f a number of rectangular thin foils of

the elements of dimensions 15X10 mm2 were placed back-to-back

(extended sample) and irradiated by 14 MeV neutrons from the

neutron generator. The experimental set-up of this

measurement is shown in Fig[4-3]. The elements and reactions

used for these measurements are shown in Table [4-1].

After irradiation, each sample was measured separately

to find its specific activity using Ge(Li)-detector. To find

the specific activity under the effect of self-absorption of

gamma-lines foils 1 and 2 were first measured, then foils 1,

2 and 3 were measured together and so on. In this case the

measured specific activity is smaller than the actual

specific activity due to the absorption of gamma quanta

within the foils.

135

sample

gamma-rays

detector

(a) good geometry

sample

gammaray

(b) bad geometry

Fig[4-2] Attenuation of gamma-rays in samples for good and

bad geometries

136

neutron beam

2 4 6

II1 3 5

foils

Fig[4-3] Irradiation of foils for self-absorption measurements

137

Table [4-1]: Reactions and elements used for measurement

element

Cu

Zn

Zr

Al

U

atomicno.Z

29

30

40

13

92

reaction used

65Cu(n#2n)64Cu

64Zn(n,p)64Cu

90Zr(n,2n)89Zr

27Al(n,a)24Na

naturallyradioactive

half-life

12.8 h

12.8 h

79 h

15.05 h

gamma linesET (KeV)

6+, 511

fi+, 511

6+, 511m909

1368

63931851001

138

The specific activities A_ were then calculated using

the expression:

N rAs " m(exp(-rtw)-exp(-r(tw+tr)))

(4.13)

where N is the peak area of the gamma line, r is the decay

constant of the product nuclide, m is the mass of the foil,

t is the cooling time and t r is the counting time (real

time). The dead-time correction for the counts under the peak

was found using the expression:

dead-time correction = t,/t (4.14)

where t, is the live-time from the MCA. The expression (4.14)

was considered sufficient to correct for dead-time due to the

low counting rate in all of these measurements.

In view of the attenuation of neutrons in the foils,

different specific activities were found relative to sample 1

(the first sample). The correction for the neutron

attenuation was done by first calculating the average

specific activity, A , using the expression:

av

n2

(4.15)

n

139

where i is the foil number and n number of foils used. The

neutron attenuation correction factors,

calculated using the expression:

:at' was then

at (4.16)

where (A )- is the specific activity of sample 1.

The specific activity ratios of the foils (1), (1 and

2), (1,2 and 3) .... relative to specific activity of foil 1

were calculated.

The results for the energy 511 KeV resulting from the Cu

samples are shown in Table [4-2]. A plot of the ratios

against the thicknesses of the foils was obtained (see

Fig[4-4]). Fitting the curve to the formula in equation

(4.12) led to a value of the effective absorption coefficient

of (0.0906 ± 0.0035 cm2/g)-

The results for the energy 511 KeV resulting from Zn

samples .are shown in Table [4-3]. A plot for the ratios

against the thicknesses of Zn samples was obtained as shown

in Fig[4-5]. Fitting the curve to the formula in equation

(4.12) led to a value of /i ff as (0.101 ± 0.007 cm2/q) .

The results for the energy 511 KeV resulting from the Zr

samples are shown in Table [4-4]. A plot for the ratios

against the thicknesses of Zr samples was obtained as shown

in Fig[4-6]. Fitting the curve to the formula in equation

(4.12) led to value of n ff as (0.1085 ± 0.0067 cm2/q).

140

Table [4-2]: Results of energy 511 KeV of Cu samples

foilsno.

1

1,2

1,2,3

1,2,3,4

1 5

1,...,6

1,...,7

3

5

7

2

4

6

s,h

0

0.2530

0.3950

0.5390

0.7080

0.5120

0.9560

1.0775

1.3310

1.6410

1.9410

2.1540

2.3720

hh

0.213

0.117

0.104

0.145

0.076

0.115

0.094

0.238

0.236

0.284

0.187

0.199

0.230

t

h

0.213

0.118

0.104

0.146

0.076

0.116

0.094

0.239

0.286

0.284

0.187

0.199

0.231

mass

g

1.198

2.397

3.593

4.807

6.027

7.206

8.424

1.196

1.220

1.219

1.199

1.214

1.179

thickness

g/cm2

0.799

1.598

2.395

3.204

4.018

4.804

5.616

area of

511 KeV

18727

18947

22278

38812

23010

39117

34692

18458

21319

20607

14130

14289

15638

yr

1352437.7

1259394.3

1119632.7

1052220.1

958833.34

907098.90

847944.50

1266534.5

1213266.4

1202441.5

1291005.3

1225699.2

1208392.8

vrafter fluxcorrection

1352437.7

1288646.6

1161806.3

1108533.6

1021499.3

974050.90

916535.20

ratios

1.00+0.01

0.952+0.010

0.859+0.007

0.819+0.008

0.755+0.007

O.72O±0.0O7

0.678+0.007

1 .2

.1—1

>

oCO

1.0

0.8

0.60 1

L

5 62 3 4thickness (g/crn2)

Fig [4-4] Attenuation of 511 KeV gamma energy in Cu samples

Table [4-3]: Results of energy 511 KeV of Zn samples

foilsno.

1

1,2

1,2,3

1,2,3,4

1,...,5

3

5

4

w

h

0

0.2030

0.4450

0.6230

0.8010

1

1.2180

1.8530

hh

0.1656

0.1951

0.1396

0.1395

0.1647

0.1967

0.2736

0.3057

h

0.1667

0.1972

0.1413

0.1414

0.1669

0.1973

0.2742

0.3062

mass

g

0.9866

1.9892

3.0090

3.9907

5.0046

1.0496

1.0139

0.9891

thickness

g/cm2

0.6577

1.3261

2.0059

2.6605

3.3364

area of

511 KeV

40180

72147

58346

62712

73875

19399

20423

16780

vr

xio3

4527.6

3462.9

2618.7

2143.6

1723.7

1882.0

1452.7

1134.5

A /r xio3

aftlr fluxcorrection

4527.6

3637.6

3018.6

2610.1

2346.7

ratios

l.bo+o.oi

0.95+0.01

0.87+0.01

0.821+0.010

0.74+0.01

.2 r -

i .. L

1.5 2.0 2.5thickness (g/em2)

5.0

Fig[4-5] Attenuation of 511 KeV gamma energy in Zn samples

A 4-M

Table [4-4]: Results of energy 511 KeV of Zr samples

foilsno.

1

1,2

1,2,3

1,2,3,4

1,...,5

1,...,6

1,...,7

3

5

7

s,h

0

2.673

14.866

18.053

19.527

20.433

21.974

23.964

26.492

39.745

hh

2.616

12.104

3.131

1.414

0.862

1.483

1.940

2.473

13.207

2.015

\

h

2.620

12.129

3.139

1.418

0.865

1.489

1.950

2.476

13.219

2.017

mass

g

0.6093

1.2204

1.8305

2.4410

2.9369

3.4328

3.9223

0.6101

0.4959

0.4895

thickness

g/cm2

0.4062

0.8136

1.2203

1.6273

1.9579

2.2885

2.6149

area of

511 KeV

25634

212965

74994

42872

30098

58620

82815

20060

83494

11655

yr

1841214

1761786

1712407

1659524

1604407

1571079

1508740

1879993

1931878

1917040

yraftlr fluxcorrection

1841214

1764795

1721993

1653623

1546273

1514251

1446682

ratios

1.00+0.01

0.958+0.008

0.935+0.009

0.898+0.00^

0.839+0.009

0.822+0.008

0.786+0.008

1.2

1.0

o

>

(0

0.8 --

0.6 L-0.0 0.5

__L__

1.0

O

O nieasiired

fitted

_ _ L ]

2.0 2.5 3.01.5

thickness (g/cm2)

Fig[4 6] Attenuation of 511 KeV gamma energy in Zr samples

In the above measurements for 511 KeV an Al-foil was put

under the sample during the counting to assure the

annihilation of the R particles.

To study the systematics of the effective absorption

coefficient, n f f / of the energy 511 KeV annihilation peak,

the /i_ff for Cu, Zn and Zr were plotted against their atomic

number. The result obtained is shown in Fig[4-7]. From this

result it can be seen that there is a linear relation between

the /*eff and the atomic number Z where:

/ieff = 0.00132XZ + 0.05668

To improve this result more measurements are needed for the

annihilation peak of elements having atomic numbers less than

28 and more than 50.

The results for the energy 909 KeV from Zr samples are

shown in Table [4-5]. A plot for the ratios against the

thicknesses of Zr is shown in Fig[4-8]. Fitting the curve of

Fig[4-8] to the formula in equation (4.12) gave a value for

M e f f of the 909 KeV of the Zr as (0.0756 ±0.0039 cm2/g)•

The results of the energy 1368 KeV from the Al samples

are shown in Table [4-6], A plot for the ratios against

thicknesses of Al samples is shown in Fig[4-9]. Fitting the

curve to the formula in equation (4.12) gives a value for

Heft as (0.0542 ± 0.0013 cm2/g)-

The results of the energy 63 KeV from Uranium [U]

147

GO

s

Oofio

-t->

CO

31)

0.2

0.1

"'"I"

o

0.025 30 4035

atomic number Z

Fig [4-7] Dependence of the attenuation coefficients of 511 KeV on the

atomic number Z

45

A

Table [4-5]: Results of energy 909 KeV of Zr samples

foilsno.

1

1,2

1,2,3

1,2,3,4

l,..-,5

1,...,6

1 7

w

h

0

2.673

14.866

18.053

19.527

20.433

21.974

\

h

2.616

12.104

3.131

1.414

0.862

1.483

1.940

t

h

2.620

12.129

3.139

1.418

0.365

1.489

1.950

mass

g

0.6093

1.2204

1.8305

2.4410

2.9369

3.4328

3.9223

thickness

g/an2

0.4062

0.8136

1.2203

1.6273

1.9579

2.2885

2.6149

area of

909 KeV

31005

260497

90963

52115

37132

72745

103517

v r

2226997.6

2155002.6

2077042.4

2017310.5

1979362.1

1949644.4

1885893.8

vrafter fluxcorrection

2226997.6

2177833.5

2119485.5

2042874.8

1998670.9

1959858.2

1872603.3

ratios

1.00+0.01

0.97.8+0.006

0.952+0.007

0.917+0.007

0.897+0.008

0.880+0.007

0.841+0.007

J-

1.2

o(0

0)

1.0

0.80.0

O measured

fitted

o

1

0.5 1.0 1.5 2.0 2.5 3.0thickness (g/cm2)

Fig [4-8] Attenuation of 909 KeV gamma energy in Zr samples

A SO

Table [4-5]: Results of energy 1368 KeV of Al samples

foilsno.

1

1+2

3

8+3

4

5+9

8+9+6

7

8+9

\

h

4.225

0

14.052

5.771

8.750

10.321

11.044

6.917

12.886

hh

1.514

3.509

14.886

1.111

1.531

0.676

0.574

1.800

0.613

h

1.515

3.514

14.892

1.113

1.532

0.678

0.576

1.801

0.614

mass

g

0.0927

0.1889

0.0921

0.2965

0.0928

0.4703

0.6751

0.0938

0.5812

thickness

g/an2

0.0618

0.1260

0.0614

0.1977

0.0618

0.3135

0.4500

0.0625

0.3875

area of

1368 KeV

5370

29537

23620

10894

4122

8112

9512

4651

8163

1043860

999337

987317.5

960311.4

976219.1

849673.4

897764.2

857019.8

913014.2

Vr

after fluxcorrection1043860

1009619.2

1005673.8

1000005.2

988535.4

1000017.9

ratios

1.0000+0.0023

0.967+0.009

0.963+0.004

0.958+0.001

0.947+0.003

0.958+0.003

1.2

O(0 1.0

0.!

O

o

0.0 0.

o

L

0.4 0.50.2 0.3

thickness (g/cm2)

Fig[4-9] Attenuation of 1368 KeV gamma energy in Al samples

Si_

Table [4-7]: Results of energy 63 KeV of U samples

foils

no.

1

1,2

1,2,3

1,2,3,

1,2,3,

1

1,....

1,....

1

4

4,5

,6

,7

,8

,9

hh

20.2101

9.4177

14.3684

9.1970

15.1096

15.3080

6.7878

5.3414

16.1125

\

h

20.2335

9.4376

14.4091

9.2288

15.1650

15.3751

6.8204

5.3687

16.1992

0

0

1

1

1

2

2

2

3

mass

g

.3624

.7171

.0740

.4327

.7966

.1533

.5134

.8776

.2354

thickn-essq/an2

0.321

0.634

0.950

1.267

1.589

1.904

2.222

2.544

2.861

area of

63 KeV

22278

11144

17578

9906

17987

20588

8652

6879

20848

specificactivity

3037.87

1646.73

1135.88

749.19

660.19

621.86

504.72

445.28

397.78

1

0

0

0

0

0

0

0

0

ratios

00+0.04

.54210.033

.374+0.020-

.247+0.018

.217+0.012

.205+0.011

.166+0.015

.147+0.014

.13U0.008

oCO

.0

0.8

0.6

0.4

0.2

0.00.0

b-

o measured

fitted

-—-a. --e—--e-—-f,

0.5 1.0 1.5 2.0thickness (g/cm2)

2.5 5.0

Fig [4-10] Attenuation of 63 KeV gamma energy in U samples

samples are shown in Table [4-7]. A plot for the ratios

against the thicknesses of U samples is shown in Fig[4-10].

Fitting of the data in Fig[4-10] to equation (4.12) was not

good. In this case the best fitting was found to be by using

the following expression:

ratio = aQ exp(-/ieffl d) + a1 exp(-/ieff2 d) (4.17)

In the case of the Uranium the energy 63 KeV was small and

the mass of each foil of Uranium was about 0.36 g. Therefore

the small energy of 63 KeV was absorbed totally within the

sample. Fitting the data of Fig[4-10] to equation (4.17) led

to a value of /x f f for the energy 63 KeV of U as (4.500 ±

0.377 cmVg).

The results for the energies 93 KeV, 185 KeV and 1010

KeV from Uranium are shown in Table [4-8].

Fig[4-11] was obtained from plotting the results for the

energy 93 KeV using equation (4.17). The M e f f of the energy

93 KeV of the U was found to be (3.060 ± 0.974 cm2/g)-

Plotting the results for the energy 185 KeV of the U and

using equation (4.17) for fitting is shown in Fig[4-12]. The

^eff o f t h e e n e r9Y 1 8 5 K e V o f u w a s found to be (1.80 ± 0.17

cm2/cj).

Plotting the results for the energy 1010 KeV of U and

using equation (4.12) for fitting is shown in Fig[4-13]. In

this case the energy was high enough to penetrate the

155

Table [4-8]: Results of energies 93, 185 and 1010 KeV of the U samples

foils no.

area of 93

As of 93

ratio of 93

area of 185

A of 185s

ratio of 185

area of 1010

A of 1010s

ratio of 1010

1

482754

65829.2

1.000+0.004

432525

58979.9

1.000+0.003

21016

2865.78

1.00±0.01

1,2

302907

44759.9

0.680+0.004

308476

45582.9

0.773+0.003

18781

2775.23

0.968+0.011

1,2,3

568685

36748.0

0.558+0.003

569618

36808.3

0.624+0.002

42027

2715.75

0.948+0.009

1,2,3,4

357772

27058.4

0.411+0.002

409040

30935.8

0.525+0.002

35338

2672.62

0.933+0.010

1,2,3,4,5

647536

23766.9

0.361+0.002

717371

26330.3

0.446+0.001

72028

2643.68

0.923+0.009

1 ,6

670418

20250.1

0.308+0.002

744489

22487.4

0.381+0.001

85903

2594.72

0.905+0.008

1 ,7

293403

17115.7

0.260+0.002

345246

20139.95

0.341+0.001

439%

2566.51

0.896+0.009

1 8

222430

14397.9

0.219+0.002

274079

17741.13

0.301+0.001

38998

2524.34

0.881+0.009

1, 9

682986

13031.4

0.198+0.001

834154

15915.71

0.270+0.001

129079

2462.84

0.859+0.008

in

OCCS

'a)

.2

1.0

0.8

0.6

0.4

0.2

0.0 L-0.0 0.5

fitted

--o

1 L 1 . . . .

.0 1.5 2.0

thickness (g/cni2)

2.5 3.0

Fig[4 11] Attenuation of 93 KeV gamma energy in U saniples

1.2

1.0

$, 0.O(0

0.6

0.4

0.20.0

.... 1 -

O.b

_ i.

1.0.J

1.b 2.0 2.5 3.0

thickness (g/cm2)

Fig[4-12] Attenuation of 185 KeV gamma energy in U samples

\S%

1.2

t

o

cti

• r - (

15

1.0 o

0 . 8 L i I....

0.0 0.5 1.0 1.5

~r 1 '

O measured

fitted

2.0 3.0

thickness (g /cm2)

Fig[4--13j Attenuation oflOlO KeV gannna energy in U samples

thickness of Uranium foils. Thus one exponential formula was

enough for fitting. The A*eff of the energy 1010 KeV of U was

found to be (0.055 ± 0.003 cm2/g)-

A comparison of the measured attenuation coefficients

'iff' and the theoretical attenuation coefficients /i-n from

reference [6] is shown in Table [4-9].

r From Table [4-9] it can be seen that Mgff is greater

j than /it_ for all the samples except U. This is because the

\ measurements were done close to the detector (bad geometry),

\ and there is about 10% - 15% difference between Meff a n d ^th"

\ In the case of Uranium, the foils used were too thick for

these low energies. Therefore the results obtained were not

good enough.

160

Table [4-9]: Comparison ofenergies.

and for some gamma

element

Cu

Zn

Zr

Al

U

atomicno.Z

29

30

40

13

92

ErKeV

511

511

511909

1368

63931851010

cm2/g t6]

0.0834

0.0843

0.08650.060

0.051'

6.8822.51.60.0779

"eff

cm2/9

0.0906 ± 0.0035

0.101 ± 0.007

0.1090 ± 0.00670.0756 ± 0.0039

0.0542 ± 0.0013

4.500 ± 0.3773.060 ± 0.9741.80 ± 0.170.055 ± 0.003

161

REFERENCES

1- G. Peto, I. Angeli and J. Csikai; Measurement of Removal

Cross-Section of Primary Neutrons for Al, Fe and Pb, IAEA

Training Course on Utalization of Neutron Generators,

Debrecen, Hungary, 1982.

2- "Activation Analysis with Neutron Generator", by S.

Nargolwalla and P. Przybylowicz, 1973.

3- S. Sudar and A. Pazsit; Measurement of the Cross-Section

for 65Cu(n,2n) Reaction, IAEA Training Course on

Utalization of Neutron Generators, Debrecen, Hungary,

1982.

4- J. Csikai; The Properties of the D-D and D-T Neutron

Sources, IAEA Interregional Training Course on Neutron

Generators, Leningrad, 25 Sep to 29 Oct 1989.

5- S. Daroczy, P. Raics; Measurement of the Yield of Short-

Li ved Fission Products by the Direct Ge(Li) Method, IAEA

Training Course on Utilization of Neutron Generators,

Debrecen, Hungary, 1982.

6- "Neutron Activation Analysis", D. De Soete, R. Gybels and

J. Hoste, 1972.

162

CHAPTER FIVE

EXCITATION FUNCTIONS MEASUREMENTS:

RESULTS AND DISCUSSION

The cross-sections for various nuclear reactions depend

on the bombarding energy of the incident particle in a highly

individualistic manner. No two are alike. Experimental

similarities between reactions are usually limited to gross

features and to general trends. The detailed dependence of

cross-sections on bombarding energy is often called the

"excitation function" or the "transmutation function" for the

particular reaction [1].

The accurate knowledge of excitation functions of fast

neutron reactions are of interest from the point of view of

nuclear reaction theory (spin distribution parameters, decay

branching ratios), design of thermonuclear devices,

applications of data in dosimetry, neutron flux

standardization, elemental analysis, etc.

Table [5-1] shows nuclear reactions for which excitation

functions around 14 MeV neutrons energy are needed.

The measured and published experimental cross-sections

for these reactions around 14 MeV show large discrepancies

[3], thus accurate measurements of the excitatin functions of

these reactions are required. Measurements for the

163

Table [5-1]: Nuclear reactions for which excitation functionswere measured

reaction

64Zn(n,p)64Cu

64Zn(n,2n)63Zn

51V(n,a)48Sc

48Ti(n/P)48Sc

1/2[2]

12.7 h

38 min

43.67 h

43.67 h

abundance%[2]

48.90

48.90

99.75

73.7

EKeV[2]

511

511670

9841751037.51212.81312.09

9841751037.51212.81312.09

IT%r

[2]

19.3

938.4

1007.4797.52.4100

1007.4797.52.4100

164

excitation functions of these reactions in the energy range

from 13.63 MeV to 14.73 MeV were performed.

5-1 Experimental Procedure:-

The irradiations of high purity Zn, V and Ti metal

samples (from Goodfellow Hetals) were performed at the

neutron generator of the Institute of Experimental Physics,

Kossuth University, Debrecen. Neutrons were produced via the

3 4H(d,n) He reaction, using 175 KeV analysed deuteron ion beam

and a target current of 150 fiA. The neutron fluence in the

position of the samples was measured by activation foils,

while the flux-variation in time was monitored by a BF3 long-

counter. Samples and monitor foils were irradiated

simultaneously with neutrons of different energies, at

different emission angles, in a scattering-free arrangement.

To decrease the energy spread of neutrons a 0.3 mm thick Al-

backed TiT target was cooled by an air-jet (i.e no water

cooling was used). The neutron energies were changed by

placing the samples and the fluence monitor foils, which were

fastened back-to-back, on an aluminium ring of 10 cm

diameter, at different angles to the direction of the

[incident deuteron beam. The irradiation time was chosen

according to the half-lives of the residual nuclei. The

Shapes of samples and the fluence monitors were rectangular,

lith dimensions of 15X10 mm2. The activities of the samples

id monitor foils were measured by an efficiency-calibrated

165

Ge(Li) gamma spectrometer, connected to an IBM compatible

computer. The fluence monitors used were Cu and Al of

thicknesses of 0.1 cm. The nuclear data of the reaction used

as fluence monitors are given in Table [5-2] [2]. The cross-

sections for the reactions used as monitors were taken from

reference [4].

In the determination of cross-sections corrections

described in chapter 4 were carried out in each case.

The cross-section measurements were performed using the

relative ratio method. The reason for doing that was the

difficulty in determining an exact absolute neutron flux

density.

If the cross-section of the sample x is CTX and the

cross-section of the fluence monitor y is av, the cross-

section ratio is given by the equation:

(5.1)

where I_ is the specific activity at the end of irradiation,

i.e.

i r

(exp(-rtw) - exp(-r(tw+tc))) m(5.2)

where I is the peak area, r is the decay constant of the

166

Table [5-2]: Nuclear data of the reactions of the fluencemonitors

reaction

65Cu(n,2n)64Cu

27Al(n,a)24Na

h

12.7

15.05

abundan-ce

%

30.8

100

Er

KeV

511

1368.532754.10

%

19.3

100100

167

residual nucleus, t is the waiting or cooling time, t is"w

the counting time and m is the mass of the foil, and

K = ed ec es (5.3)

where e is the energy peak detector efficiency, e, is the

dead-time correction, e is the cascade correction, e is thec s

self-absorption correction and IT is the absolute gamma

yield; A is the atomic weight, f is the isotopic abundance

and S is the saturation factor, which includes the correction

of the variation of the flux during the irradiation [5].

If the fluence monitor y gives the same residual nucleus

as the sample x, equation (5.1) simplifies to the form:

(5.4)

In equation (5.4) the cross-section a is easy to

calculate and the statistical error is smaller, due to the

disappear of many factors present in equation (5.1).

Therefore the use of the relative method in the case of

equation (5.4) should give more accurate results.

5-2 The Excitation Function of 64Zn(n,p) Cu Reaction:-

The excitation function of the reaction 64Zn(n,p) Cu

was measured in the energy range 13.63 MeV to 14.73 MeV using

168

the neutron generator of the Institute of Experimental

Physics, Debrecen, Hungary. The half-life of this reaction is

12.7 hours and the percentage branching of R emitted from

Cu is 19.3 %. The gamma-ray used for the cross-section

measurement was the positron annihilation of energy 511 KeV.

The reaction used for absolute normalization is the

Cu(n,2n) Cu, which gives the same residual nucleus Cu as

of the sample. This made the calculations easier and

decreased the corrections needed for the measurement.

The rectangular samples and monitors were fastened back-

to-back in the Al-ring as shown in Fig[5-1]. The angles used

are shown in Table [5-3]. The irradiation time was 2 hours.

During counting by the Ge(Li) detector the samples and

the monitors were sandwiched between two Al-foils to assure

the annihilation of the 6+ emitted before arriving the

detector.

An interfacing reaction appearing in the Cu monitor is

the following:

63Cu(n,2n)62Cu (5.5)

with a product nucleus half-life of 9.76 min and target

abundance of 69.2% . Cu is a 6 emitter, and therefore will

interfere with the Cu(n,2n) Cu reaction. To get rid of

this interference a long waiting time of about 2 hours was

169

air iet

TiT target

D beam

Fig[5-1] The experimental set-up for irradiation of Zn-foils with Cu monitors

170

Table [5-3]: Angles used for irradiation of Zn-foils

angledegree

0°

40°

70 s

90°

110°

130°

140°

foils

Z nl

C ul

Zn2

C u2

Zn3

cu3

Z n4

CU4

Zn5

Cu5

Zn6

Cu6

Zn?

Cu7

massg

0.94598

1.22977

0.92192

1.22835

1.01619

1.21721

0.94324

1.22232

0.96067

1.21634

1.01994

1.22992

1.01994

1.22992

171

used for the Cu-monitor foils before start of counting.

An interference that might affect the reaction

Zn(n,p) Cu in the Zn sample is associated with

Zn(n,2n) Zn reaction, which is a 6+-emitter also, with a

half-life of 38 min. To get rid of this reaction a long

waiting time of about 2 hours was used for Zn-samples before

start of counting.

The background in the 511 KeV peak was measured for 68

hours and was found to be 25 c/h.

The self-absorption corrections were done for Zn and Cu

foils, using effective self-absorption coefficient of 0.101

and 0.0906 for Zn and Cu, respectively. Other corrections for

the Cu foils involve flux depression due to absorption by Zn

foils and the distance of 0.1 cm between the Zn and Cu foils.

These corrections were done using the formula:

:flux expt-M

(5.6)

where az is the microscopic removal cross-section equal 1.68

barn [9], N is the Avogador's number, d™ is the thickness

of Zn-foil in g/cm2 and M is the atomic weight of Zn. The 4.9

cm and 5 cm were the distances of Zn and Cu, respectively,

from the target.

The atomic weight of Zn and Cu are 65.38 and 63.546,

respectively [20],

172

The result of Zn and Cu measurements obtained are shown

in Table [5-4].

The energy of neutrons at different emission angles

using a deuteron energy E,=175 KeV for the neutron generator

at the Institute of Experimental Physics, Debrecen, Hungary,

was found using the eguation (5.7):

E n (MeV) = E Q + E± cose + E 2 cos 9 (5.7)

where 9 is the neutron emission angle and the parameters E Q

is 14.09352, Ex is 0.62200 and E 2 is 0.01765 [7]. The neutron

energies at the angles used for the irradiation of samples

and monitors are shown in Table [5-5].

The cross-section of the reaction Cu(n,2n) Cu in the

neutron energy range from 13.63 MeV to 14.73 MeV were found

from reference [4]. Using these cross-sections and the cross-

section ratios of 64Zn(n,p)64Cu to 65Cu(n,2n)64Cu from Table

[5-4], the cross-sections of the reaction Zn(n,p) Cu were

calculated in the neutron energy range from 13.63 MeV to

14.73 MeV. These cross-sections are shown in Table [5-6].

If the cross-sections given in Table [5-6] are plotted

against the neutron energy a curve called the excitation

function is obtained. The excitation function for the

Zn(n,p) Cu reaction, is shown in Fig[5-2].

The analytical statistical multistep-direct/statistical

multistep-compound (SMD/SMC) model presented in chapter 2

173

Table [5-4]: Results for the ratios of the Zn(n,p) to the Cu(n,2n) reactions cross-sections

foils

CuZ nl

C U2Zn22

CuZn3

3

C U42 n4

CuZn5

?*Z n6

Zn?

h

01.9381

02.8017

015.1369

017.3992

020.0892

0.22.6189

02.9114

lc

h

0.22741.1037

0.248712.5974

0.24922.5033

0.31123.0006

0.31622.8185

0.36462.2329

0.593112.2134

area of

511 KeV

61985579

699544456

69347052

85597323

83536516

94614909

356814910

408875.18112166.88

422569.53113027.60

422000.60124167.80

416080.35132858.90

401537.31142422.35

3905%. 32144179.73

98455.8038635.90

self-abso.correction

W£Zn

0.9831

0.9818

0.9880

0.9834

0.9829

0.9875

0.9875

fluxcorrection

0.9511

0.9513

0.9504

0.9511

0.9509

0.9503

0.9493

ratio

0.16676 ± 0.00320

0.16242 ± 0.00220

0.17962 + 0.00320

0.19417 ± 0.00330

0.21555 ± 0.00390

0.22521 ± 0.00430

0.23730 + 0.00470

Table [5-5]: Neutron energy at various emission angles

angle

0°

40°

70°

90°

110°

130°

140°

neutron energy E MeV

14.73 ± 0.05

14.58 ± 0.05

14.31 ± 0.05

14.09 ± 0.05

13.88 ± 0.05

13.70 ± 0.05

13.63 ± 0.05

175

Table [5-6]: Cross sections of 64Zn(n,p)64Cu for E =13.63 to14.73 MeV

En

MeV

14.73

14.58

14.31

14.09

13.88

13.70

13.63

cross-sectionratio

0.1668±0.0032

0.1624±0.0022

0.1796±0.0032

0.1942±0.0033

0.215510.0039

0.2252±0.0043

0.2373±0.0047

a65Cu(n,2n)64Cu

mb

964.35±59.00

954.91158.00

928.50157.00

907.09+54.00

879.47+53.00

853.56+52,00

842.04150.00

a64Zn(n,p)64Cu

mb

160.854110.314

155.07719.651

166.759+10.660

176.157+10.906

189.526111.925

192.222+12.272

199.816112.508

176

250 r —

200

150 -

100

U

o measured

LJ ref.3

UXIFONn

LJ

13.6 13.8

•

J L J !_.-.

14.0 14.2 14.4 14.6

n e u t r o n e n e r g y (MeV)

14.J

2] Zn — 64(n,p) excitation function

[8-10] was applied for comparison of the experimental results

given in Fig[5-2]. Both the SMD and the SMC parts were

calculated by the same residual interaction. The calculations

were performed with a global parameter set which describes

emission data at energies up to 80 MeV. However, since at

lower energies shell-structure effects become important and a

description using only one global parameter set for the whole

mass range (A>20) is not possible, one free parameter was

introduced-the pairing shift S.

Calculations were performed with the code EXIFON

(version 2.0) using the following global parameters [11-15]:

strength of surface-delta interaction FQ = 27.5 MeV; radius

parameter, rQ = 1.21+4.0 A~2//3-15 A~4/3 fm; potential depth,

VQ = 52-0.3 E MeV; Fermi energy, E p = 33 MeV; optical model

potential, Wilmore and Hodgson, for neutrons.

Here, the single-particle state density of bound

particles (and holes) was taken as g = 4d(Ep), where

d(EF) =(27rh/)~3

is the common state density in the nuclear volume V=4wR /3

and R=rQA1/4.

The pairing effects were taken into account by using the

ef feffective binding energies B_ . For a system of A=N+Zc

nucleons the effective neutron (proton) binding energy is

defined as:

178

and

= B

n5n f o r

B e f f = B + 6_ for

odd

even

odd

even

N (5.8)

N (5.9)

where B , * is the exact neutron (proton) binding energy. The

standard pairing shift is [16]:

= S - 12.8 A "* MeV

The only free parameter in the present calculations is

S , and the value (in MeV) used for Zn isotope is 1.4.

The calculated cross-sections of the reaction

Zn(n,p) Cu using the EXIFON code at different neutron

energies are shown in Table [5-7].

The excitation function of Zn(n,p) Cu reaction using

the theoretical calculation with the EXIFON code is shown in

Fig[5-2].

5-2-1 Discussion:-

In these measurements the relative values of a(n,p) for

Zn were determined around 14 MeV using the "well known"

cross-sections for the reaction Cu(n,2n) Cu, for

normalization, with the same residual nucleus.

The cross-section values obtained by the relative method

179

Table [5-7]: Calculated cross-sections of Zn(n,p) Cu usingEXIFON code

E n MeV

14.7

14.5

14.3

14.1

13.9

13.7

64Zn(n,p)64Cu a(mb)

137.70

147.56

157.96

168.92

180.40

192.40

180

were compared with the literature data [3]. The literature

data shows large discrepancies in determining the excitation

function of Zn(n,p) Cu reaction.

The recommended cross-sections for the reaction64Zn(n,p)64Cu, at energies 14.1 MeV and 14.5 MeV, by the

International Atomic Energy Agency in reference [22] are 200

mb and 185 mb respectively. The present work give values of

176 mb and 158 mb at the same energies, which might change

the recommended values by 12% and 14% respectively. The

neutron activation analysis cross-section recommended value

in reference [17], for this reaction at 14.1 MeV is, 220 mb;

thus the present work might change this value by 25%.

It can be observed that in the present measurement the

measured excitation function and the calculated values using

EXIFON code are in good agreement. This can be attributed to

the successful choice of the pairing shift in the SMD and SMC

(n,p) reaction channels.

The estimated statistical error for these measurements

does not exceed 7%.

The use of the relative method for determining the

cross-section with the reference monitor leading to the same

residual nucleus, makes the calculations simple and the

measurements more accurate.

181

5-3 The Excitation Function of Zn(n,2n) Zn Reaction:-

The excitation function of the reaction Zn(n,2n) Zn

was measured in the energy range 13.70 MeV to 14.73 MeV.

The half-life of Zn is 38.1 min and the gamma energy

used for the cross-section measurement was the annihilation

511 KeV peak. The percentage branching of the B emitted from

63Zn is 93%.

The reaction used for absolute normalization is the

Cu(n,2n) Cu which is a 6 emitter. Using this reaction

helps in reducing the effect of the detector efficiency

because Zn and Cu give the same 511 annihilation peak,

and the efficiencies cancel out.

The rectangular samples and the monitors were fastened

back-to-back in the Al-ring as shown in Fig[5-1]. The samples

and monitors used are similar to those used in determining

the excitation function of Zn(n,p) Cu reaction. The angles

used for the measurements are shown in Table [5-3]. The

irradiation time was 2 hours. For the assurance of the

annihilation of the emitted B two Al-foils were used as

before.

The Zn(n,2n) Zn reaction has an interference from

64 64 +

Zn(n,p) Cu reaction which is also 6 emitter, with a half-

life of 12.7 hours and a branching of 6 of 19%. Since the

reaction Zn(n,2n) Zn has a half-life of 38 min and a 6

branching of 93% a small waiting time (less than 40 min) will

be enough to subtract the contribution of 511 KeV which comes

182

64

from Cu.

Let N be the count of the 511 KeV peak from

Zn(n,p) Cu reaction after an appropriate waiting time, and

NQ is the count of 511 KeV from 64Zn(n,p)64Cu immediately at

end of irradiation which contribute to the 511 KeV count from

Zn(n,2n) Zn reaction. Thus we have the following relation

for the count NQ:

exp(-rtwQ)

exp(-rtwp)

(l-exp(-rtc0))

(l-exp(-rtcp))

CO

T tIP cp

] (5.10)

where t Q is the small waiting time immediately following

irradiation, t is the appropriate waiting time; t _, twp cu ^P

are the real counting times after small and appropriate

waiting times respectively; T,_, T, are the live counting

times after small and appropriate waiting times respectively

and r is the decay constant of Cu.The results of the contribution of Cu count to the

63Zn count is given in Table [5-8],

The background of the 511 KeV peak (of about 25 c/h) was

subtracted from each measurement.

The self-absorption correction, and the flux correction

for Cu foils, were done similar to the previous measurements.

Due to the different half-lives of the 63Zn and 64Cu a

BF3 long counter was used to correct for the variation of the

183

Table [5-8]: Contribution of Cu counts to the Zn counts

sample

(Znl)o

<ZVP

<Zn2>0

<zn2>p

(Zn3)Q

<Zn3>p

(Zn4>o

<zn4>p

(Zn5)Q

<Zn5>p

(Zn6>o

(ZVp

h

0

5.7497

0

6.7686

0

19.3336

0

21.7561

0

24.6525

0

27.3694

Tl

h

0.0961

1.1034

0.0864

12.5956

0.0959

2.5028

0.1111

3.0001

0.1329

2.8181

0.2034

2.2327

h

0.0965

1.1037

0.0867

12.5974

0.0962

2.5033

0.1114

3.0006

0.1331

2.8185

0.2037

2.2329

areaafterl o n9 fcw

5605

44456

7052

7323

6516

4909

ratioN o / N

P

0.1225

0.0137

0.1175

0.1312

0.1947

0.4286

No

684

608

828

961

1268

2104

184

neutron flux, with the neutron fluence taken every 10 mins.

The readings are shown in Table [5-9]. Applying the flux

correction formula to the data in Table [5-9], the flux

correction term S U/S n in equation (5.1) was found to be:

_Cu/cZn _ n , KniS /S = 0.1501

(5.11)

We see from the decay scheme of Zn in Fig[5-3] that

there are two cascades between the 6 -decay and the gamma

lines 962 KeV and 669 KeV. The cascade correction is given

by:

6.3x93(l-6ec = s 9 6 2

8.1x93(l-(es669

(6.3+8.1)x93(5.12)

where e is the self-absorption for 669 KeV and 962 KeV gamma

lines and eT is the total detector efficiency for the 669 KeV

and 962 KeV gamma lines [2]; where e s 6 6 9 = 0.9654, e S9 6 2 =

0.9807 [17]; e T 6 6 9 =0.0945 and e T 9 6 2 =0.1129 [18]. Thus the

cascade correction factor e is 0.9003.

The results of Zn and Cu measurements are shown in

Table [5-10],

The cross-sections of the reaction Zn(n,2n) Zn were

calculated using the reference cross-section of the reaction

Cu(n,2n) Cu [4] and the cross-section ratios given in

Table [5-10]. The results for the Zn(n,2n) Zn reaction

185

Table [5-9]: Readings of BF_ long counter for neutron fluence

timemin

10

20

30

40

50

60

70

80

90

100

110

120

neutron fluence counts

3181032

3114301

2697850

2418370

2050450

1716940

1547740

1377530

1277900

1126310

948760

805880

186

63

962 KeV

669 KeV

6.3 I

8.11

84 I

Zn

Fig [5-3] The decay scheme of Zn

187

Table [5-10]: Results for the ratios of the Zn(n,2n) to the Cu(n,2n) reactions cross-sections

foils

ZnCu!

Zn2

ZnCU3

Zn4

ZD5

0.3.

0.4.

0.4.

0.4.

0.5.

05

h

06338750

17141378

26924658

37867356

50690703 '

65074072".

0.0.

0.0.

0.0.

0.0.

0.0.

0.0.

fcc

h

09652274

08672487

09622492

11143111

13313162

20373646

area of

511 KeV

195556198

148836995

145086934

125748559

110008353

124409461

244777.0127571.76

236042.7528906.76

210335.9529389.51

192643.6629406.78

161004.7828902.19

136073.8028636.56

self-abso.correction

W€Zn

0.9831

0.9818

0.9880

0.9834

0.9829

0.9875

fluxcorrection

0.9511

0.9513

0.9504

0.9511

0.9509

0.9503

0.

0.

0.

0.

0.

0.

ratio

18521 ± 0.00500

17157 ± 0.00470

15118 ± 0.00420

13784 + 0.00380

11714 + 0.00380

10032 ± 0.00280

ooOOX

cross-sections are shown in Table [5-11].

The excitation function of the reaction Zn(n,2n) Zn

is obtained by plotting the cross-section versus the neutron

energy, as shown in Fig[5-4].

The experimental results obtained in Fig[5-4] were

compared with the theoretical calculations using the EXIFON

code (version 2.0) [11]. The global parameters set indicated

for the Zn(n,2n) Zn reaction were used. The only free

parameter in the present calculations was 6 , and the value

(in MeV) used for Zn isotope was -0.4, instead of zero for

the (n,2n) channel.

The calculated cross-sections of the reaction

Zn(n,2n)63Zn using EXIFON code at different neutron

energies are shown in Table [5-12]. The excitation function

of Zn(n,2n) Zn reaction for the the<

using EXIFON code is shown in Fig[5-4].

of Zn(n,2n) Zn reaction for the theoretical calculations

5-3-1 Discussion:-

In these measurements the relative values of a(n,2n) for

Zn were determined around 14 MeV using the "well known"

cross-section of Cu(n,2n) Cu for normalization.

The cross-section values obtained by the relative method

were compared with the literature data [3]. Some of the

literature data agreed well with the measured excitation

function, others showed some discrepancies and did not agree

so well. However, not much data were found.

189

64 63fable [5-11]: Cross sections of Zn(n,2n) Zn reaction forE n =13.7 to 14.73 MeV

I EnMeV

14.73

14.58

14.31

14.09

13.88

13.70

cross-sectionratio

0.185210.0050

0.1716±0.0047

0.1512±0.0042

0.1378±0.0038

0.117110.0038

0.100310.0028

65Cu(n,2n)64Cu

a(mb)

964.35159.00

954.91+58.00

928.50+57.00

907.09154.00

879.47153.00

853.56152.00

64Zn(n,2n)63Zn

a(mb)

178.600111.784

163.863+10.918

140.389+9.460

124.99718.201

102.986+7.049

85.61215.737

190

250

200

ao

o0)wIt»

O

o

150

00

o measured

a ref. 3

- - - KXIKON

5 0 L - •115.6

i

.5.8

nn

L"J

n

4.4

D

L ..

14.6

G

14.814.0 14.2

neutron energy (MeV)

5 4] Zn 64(n,2n) excitation function

5.0

M

Table [5-12]: Calculated cross-sections of Zn(n,2n) Znusing EXIFON code

E n MeV

14.7

14.5

14.3

14.1

13.9

13.7

64Zn(n,2n)63Zn a(mb)

168.42

152.94

136.84

119.25

102.74

86.26

192

The recommended cross-sections for the reaction

64Zn(n,2n)63Zn, at energies 14.1 MeV and 14.5 MeV, by the

International Atomic Energy Agency in reference [22] are 119

mb and 165 mb respectively, The present work give values of

125 mb and 150 mb at the same energies, which might change

the recommended values by 5% and 9% respectively. The neutron

activation analysis cross-section recommended value in

reference [17], for this reaction at 14.1 MeV is, 155 mb;

thus the present work might change this value by 19%.

The measured excitation function and the calculated

values using EXIFON code were in good agreement and this was

achieved mainly through changing the pairing shift in the SMD

and SMC (n,2n) reaction channels. The (n,2n) reaction cross-

sections can be well defined by EXIFON code.

The estimated statistical error for these measurements

does not exceed 7%.

c 1 A Q

5-4 The Excitation Function of V(n,a) Sc Reaction:-

The excitation function of the reaction V(n,a) Sc was

measured in the energy range 13.70 MeV to 14.73 MeV.

The half-life of the product nucleus in this reaction is

43.67 hours, and the emitted gamma energy that was used for

the cross-section measurement is 984 KeV, of intensity 100%.

The reaction used for absolute normalization was27 24Al(n,a) Na. The half-life of the product nucleus in this

reaction is 15.03 hours, and the gamma line used is

193

1368.5 KeV, of intensity 100%.

The rectangular samples and monitors were fastened back-

to-back in the Al-ring, as shown in Fig[5-5]. The angles used

are shown in Table[5-13]. Irradiation time was 2 hours.

The self-absorption correction for each foil was

calculated using the effective self-absorption coefficient,

/i f f, as given in Table [5-14] [19].

The flux correction for the Al-foil due to neutron

removal by the V foil, and flux depression through the

distance 0.04 cm between the V and Al foils was done using

equation (5.13).

€flux = (4.7/4.74)2 exp(-av Ny dy/M) (5.13)

where av is the microscopic removal cross-section in barns;

av is 1.34 barn [6], dv is the thickness of V foils, M is the

atomic weight of V and N is the Avogador's number. The 4.7

cm and 4.74 cm were the distances of V and Al foils,

respectively from the T-target. The atomic weight of V and Al

are 50.94 and 26.98, respectively [20].

Due to the different half-lives of the 48Sc and 24Na a

BF3 long counter was used to correct for the variation of the

neutron flux. The readings are shown in Table [5-9]. The flux

correction term using equation (5.1) for S /S was found to

be 2.8181.

194

T-target

Fig[5-5J The experimental set-up for irradiation of V, AI and Ti foils

Table [5-13]: Angles used for irradiation of V foils

angledegree

0°

40°

70°

90°

110°

130°

foils

vl

A ll

V2

A 12

V3

Al3

V4

Al4

V5

Al5

V6

A 16

massg

0.2252

0.3985

0.2295

0.3976

0.2272

0.3983

0.2229

0.3981

0.4524

0.3966

0.4551

0.3769

196

Table [5-14]: The Meff values for V and Al samples

element

V

Al

gamma energyKeV

175.4

984.0

1037.0

1312.1

1368.5

2754.0

jueff (cm2/g)

0.0714

0.1003

0.1053

0.0915

0.0540

0.0374

197

From the decay scheme of Sc shown in Fig[5-6], a

number of cascade gammas with the 984 KeV line can be

observed. The cascade correction for the energy 984 KeV was

found using the formula of the cascade correction of equation

(4.9) and substituting for the following values in the

48

formula [18]; the total efficiencies of Sc lines are eT(175

KeV) is 0.1068, eT(1037 KeV) is 0.1173 and eT(1312 KeV) is

0.1378. Also the effective self-absorption coefficients Meff

from Table [5-14] were used. The cascade correction for the48

energy 984 KeV of Sc was found to be 0.7562.24As shown in the decay scheme of Na given in Fig[5-7],

the line 2754 KeV is in cascade with the line 1368.5 KeV. The

cascade correction for 1368.5 KeV was found using the cascade

correction formula (4.9) and the following data: the total

efficiency of 2754 KeV is 0.1935 and the self-absorption

correction that was calculated using the A*eff of 2754 KeV in

Table [5-14]. Thus the cascade correction e of the energy

1368.5 KeV was found to be 0.8075. The photopeak efficiencies

for the energies 984 KeV and 1368.5 KeV are 0.0072 and 0.005,

respectively [18].

The results for the ratios of the cross-sections of the

reactions are given in Table [5-15].27 24

The cross-sections of the reaction Al(n,a) Na in the

energy range 13.70 MeV to 14.73 MeV were found from reference[4]. Using these cross-sections and the cross-section ratiosV Ala /a in Table [5-15], the cross-sections of the reaction

198

48Sc

P" 9.3/ 175.35 (76/) KeV

90.7/ 1037.5 KeV

1312.1 KeV

984 KeV

48Fig [5-6] The decay scheme of Sc

199

24Na

P"99% 2754 KeV

0.003% 1368.5 KeV

24Mg

24Fig [5-7] The decay sheme of Na

200

51 27Table [5-15]: Results for the ratios of the V(n,a) to the Al(n,a) reactions cross-sections

foils

Al

hl

AlV22

Al,

' , '

U,

' 4

U,

'5

U 6'6

t.wh

0.881130.2911

1.397253.2008

1.978377.5708

2.450398.9856

1.19001.4208

12.274223.6294

tc

h

0.505614.8885

0.564515.3417

0.456221.3911

0.460342.0305

0.223410.8289

0.591513.8840

area ofthe peak

41451562

47771127

40791036

42121236

32135221

50694473

Isp. activity

21698.37845.89

23021.59839.11

24878.83860.87

26039.73869.62.

38618.281186.80

40670.521147.88

self-abso.correction

0.98580.9851

0.98580.9848

0.98580.9849

0.98580.9852

0.98580.9702

0.98650.9700

fluxcorrection

V*Al

0.9788

0.9787

0.9788

0.9788

0.9622

0.9622

ratio

V Rlts Its

0.1517 + 0.0071

0.1413 ± 0.0075

0.1341 ±0.0074

0.1294 ± 0.0076

0.1185 + 0.0034

0.1089 ± 0.0041

51V(n,a)24Na in the energy range 13.70 MeV to 14.73 MeV were

calculated. The results are shown in Table [5-16],

Plotting the neutron energy against the cross-sections

of V(n,a) Sc in Table [5-16], the excitation function of

the V(n,a) Sc reaction was obtained, as shown in Fig[5-8].

To compare the results obtained in Fig[5-8] with the

theoretical calculations the EXIFON code (version 2.0) [11]

was used. The global parameters set indicated for the

Zn(n,p) Cu reaction were used. The only free parameter in

48the present calculations was 6 , and the value used for Sc

isotope was 0.45 MeV, instead of zero.

The calculated cross-sections of the reaction

V(n,a) Sc using EXIFON code at different neutron energies

are shown in Table [5-17].

The excitation function of 51V(n,a) Na reaction using

theoretical calculations with EXIFON code is shown in Fig[5-

8], for comparison with the experimental results and other

values found in the literature.

5-4-1 Discussion:-

In these measurements the relative values of the cross-

sections of the reaction V(n,o) Sc were determined around

14 MeV using reaction of "well known" cross-section

27 24Al(n,a) Na as a standard.

The cross-section values obtained by the relative method

were compared with some literature data. The

202

Table [5-16]: Cross sections of V(n,a) Sc reaction for E=13.7 to 14.73 MeV n

En

MeV

14.73

14.58

14.31

14.09

13.88

13.70

cross-sectionratio

0.1517±0.0071

0.1413±0.0075

0.1341±0.0074

0.129410.0076

0.1185±0.0034

0.108910.0041

z/kl(n,a) *Na

a(mb)

116.3910.58

118.2010.59

121.3910.61

123.5310.62

125.4110.63

126.58+0.63

51V(n/a)48Sc

a(iab)

17.66010.831

16.69610.890

16.276+0.902

15.98210.942

14.86410.430

13.79010.524

203

20

o 16CDV)I

ouu

14( )

C)

• •

()()

•

•()

C) •

D

•

o

•

-

measured

EXIFON

Ref.[3]

Ref[21]

213.6 13.8 14.0 14.2 14.4 14.6 14.8 15.0

neutron energy(MeV)

Fig[5 —8] V —51(n,a) exci ta t ion function

Table [5-17]: Calculated cross-sections of V(n,a) Sc usingEXIFON code

E n MeV

14.7

14.5

14.3

14.1

13.9

13.7

51V(n,a)48Sc a(mb)

17.44

16.60

15.79

14.98

14.20

13.44

205

literature data of reference [3] were observed to show a wide

spread and were not in good agreement with the present

measurements. The more recent data of reference [21] showed

excellent agreement with the present measurements.

The recommended cross-sections for the reaction

51V(n,a)48Sc, at the energies 14.1 MeV and 14.5 MeV, by the

International Atomic Energy Agency in reference [22] are 15

mb and 17 mb respectively. The present work is in good

agreement with these recommended values, 16 mb and 16.6 mb,

at the specified energies. The neutron activation analysis

cross-section recommended value in reference [17], for this

reaction at 14.1 MeV is 40 mb, thus the present work might

change this value by 60%.

The measured excitation function and the calculated one

using EXIFON code were in good agreement. This was attained

mainly through changing the pairing shift in the SMD and SMC

(n,a) reaction channels.

The statistical error calculated for these measurements

is expected not to exceed 6%.

5-5 The Excitation Function of Ti(n,p) Sc Reaction:-

The excitation function of the reaction Ti(n,p) Sc

was measured in the energy range 13.70 to 14.73 MeV of the

neutrons produced by the neutron generator.

The reaction used for absolute normalization is

27 24Al(n,a) Na as in the last case.

206

NEXT PAGE(S)••ft BLANK

Table [5-18]: Angles used for irradiation of Ti foils

angledegree

0°

40°

70°

90°

110"

130°

foils

T il

A 11

Ti3

A 12

Ti5

Al3

Ti?

Al4

Tig

Al5

Tlll

A16

massg

0.2686

0.3985

0.2680

0.3976

0.2686

0.3983

0.2685

0.3981

0.2685

0.3966

0.2663

0.3769

208

i!

Table [5-19]: BF3 long counter readings

timerains

8

16

24

32

40

48

56

64

72

80

88

96

104

112

120

BF_ readings

6023170

5671890

5236770

5164140

4819690

4854840

4864720

4786380

4714240

4339360

3479220

4114850

4129070

4011150

3747500

209

Table [5-20]: Results for the ratios of the Ti(n,p) to the Al(n,a), reactions cross-sections

foils

TilUl

Ti3M2

T i5Ai

Ti

KTigAI

TillR 16

h

13.12500.0542

18.73000.3842

37.53670.6839

47.28070.9778

62.35251.1900

70.944712.2742

tc

h

5.58350.3194

4.88320.2922

9.72040.2793

15.04610.2044

8.57650.2237

15.86820.5915

peakarea

41093684

33853558

50583516

64472898

28723213

43845069

Isp. activity

3527.8929373.24

3619.6531480.82

3794.3932919.82

3920.1837529.79

3588.%38618.28

3619.5140670.52

self-abso.correction

0.9822

0.9818

0.9880

0.9834

0.9829

0.9875

fluxcorrection

0.9511

0.9513

0.9504

0.9511

0.9509

0.9503

ratio

0.18521 + 0.00500

0.17157 + 0.00470

0.15118 i 0.00420

0.13784 ± 0.00380

0.11714 ± 0.00380

0.10032 ± 0.00280

The cross-sections of the reaction Ti(n,p) Sc were

Ti Alfound using the cross-section ratios (a /a ) of Table [5-

20] and the known cross-sections of the reaction

Al(n,a) Na from reference [4] in the energy range 13.70 to

14.73 MeV. The results for the cross-sections of

Ti(n,p) Sc reaction are shown in Table [5-21].

Plotting the cross-sections of Ti(n,p) Sc versus the

neutron energy from Table [5-21], the excitation function of

this reaction was obtained, as shown in Fig[5-9].

The results for the measured excitation function were

compared with the theoretical calculations using EXIFON code.

The global parameter set indicated earlier for Zn(n,p) Cu

reaction were used. The only free parameter in the present

calculation was S , and the value (in MeV) used for Sc

isotope was -0.4 instead of -1.83. The calculated cross-

sections are given in Table [5-22]. The excitation function

of Ti(n,p) Sc reaction using the theoretical calculations

is shown in Fig[5-9].

5-5-1 Discussion:-

In these measurements the relative values of a(n,p) for

Ti were determined around 14 MeV using the "well known"

cross-sections for Al(n,a) Na reaction around 14 MeV as

standards.

The cross-section values obtained by the relative method

were compared with literature data. The literature data in

211

48 48Table [5-21]: Cross sections of Ti(n,p) Sc reaction for

E n =13.70 to 14.73 MeV

En

MeV

14.73

14.58

14.31

14.09

13.88

13.70

cross-sectionratio

0.5888±0.0022

0.563610.0022

0.565110.0021

0.511910.0019

0.491610.0021

0.470910.0019

27Al(n,a)24Na

a(mb)

116.3910.58

118.2010.59

121.3910.61

123.5310.62

125.41+0.63

126.58+0.63

48Ti(n,p)48Sc

a(mb)

68.53012.630

66.61812.610

68.59812.584

63.23512.393

61.65212.689

59.607+2.361

212

80

70

oCDOTI

<z>m£ 60o

50

o—

measured

EXIFON

Ref.[3]

•

D

3.6 13.8 14.0 14.2 14.4 14.6neut ron energy(MeV)

14.8 15.0

Fig[5-9] Ti-48(n,p) excitaion function

2 ( 3

48 48Table [5-22]: Calculated cross-sections of Ti(n,p) Scusing EXIFON code

EnMeV

14.7

14.5

14.3

14.1

13.9

13.7

48Ti(n,p)48Sc a(mb)

66.00

64.64

63.42

62.32

61.07

59.76

214

reference [3] showed large discrepancies and were not in good

agreement with the present measurements.

The recommended cross-sections for the reaction

48Ti(n,p)48Sc, at the energies 14.1 MeV and 14.5 MeV, by the

International Atomic Energy Agency in reference [22] is 61

mfc>. The present work give values of 63.2 mb and 65 mb at the

same energies, which might change the recommended values by

4% and 6% respectively. The neutron activation analysis

cross-section recommended value in reference [17], for this

reaction at 14.1 MeV is 90 mb, thus the present work might

change this value by 30%.

The measured excitation function and the calculated one

using EXIFON code were in good agreement. They exhibited the

same trend, and this was achieved mainly by changing the

pairing shift in the SMD and SMC (n,p) reaction channels.

The statistical error calculated for these measurements

is not expected to exceed 5%.

5-6 Conclusion:-

The excitation functions for some reactions were

measured using the neutron activation technique with good

statistics and a high degree of precision. The measurements

were in good agreement with theoretical calculations using

the EXIFON code. However, not so good agreement was observed

with some of the literature data. The measurements were

carried out for various neutron energies around 14 MeV

215

produced by the D-T neutron generator.

The EXIFON code calculations gave good results for (n,p)

and (n,a) reaction cross-sections. However, it was found to

describe the (n,2n) reaction cross-sections much better than

the other reactions.

!

il

216

REFERENCES

"The Atomic Nucleus", Robley D. Evans, MCGRAW-HILL Book

company, 1955, p441.

"Table of Isotopes" 7th Edition, Edgardo Browne, Janis M.

Dairiki and Raymond E. Doebler, A Wiley-Interscience

Publication, 1978, pl93.

"Neutron Cross-Sections and Neutron Cross-Section Curves"

Volume 2, Victoria Mclane, Charles L. Dunford and Philip

F. Rose, Academic Press Inc. San Diago, 1988.

D. E. Cullen; ENDF Pre-Processing Codes, IAEA Nuclear Data

Section, Vienna, Austria, April 1991.

J. Csikai; The properties of D-D and D-T Neutron Sources,

IAEA Interregional Training Course On Neutron Generators,

Leningrad 25 Sep.-29 Oct. 1989.

"Activation Analysis With Neutron Generators", Sam S.

Nargolwalla and Edwin P. Przyblowicz, John Wiley and Sohs,

1973, pl61.

"HandBook of Fast Neutron Generators" volume 1, J. Csikai,

CRC Press INC., 1987, pl8.

H. Kalka, M. Torjman and D. Seeliger, Phys. Rev. C40,

1619(1989).

H. Kalka, M. Torjman, H. N. Lien, R. Lopez and D.

Seeliger, Z. Phys. A335, 163(1990).

- H. Kalka, Z. Phys. A (in press).

217

H. Kalka; EXIFON- A Statistical Multistep Reaction Code

(1990), NEA Data Bank, Saclay, France.

A. Faessler and Fortscher, Phys. 16, 309(1968).

I. Angeli, J. Csikai and A. Algora Pineda, Proceedings of

the 17th International Symposium on Nuclear Physics,

Gaussig, Zentralinlinstitut fur Kernforschung, Report ZfK

646(1987), pl03.

"Nuclear Structure" Volume 2, A. Bohr and B. R.

Mottelson, Benjamin, New York, 1957.

A. Chatterjee, K. H. N. Murthy and S. K. Gupta, Pranama

16, 391(1981).

W. Dilage, W. Schantl, H. Vonach and M. Uhl, Nucl. Phys.

A217, 269(1973).

"Neutron Activation Analysis" Volume 34, D. De Soete, R.

Gybels and J. Hoste, Wiley Interscience, 1972.

J. Csikai, Cs. M. Buczko, Institute of Experimental

Physics, Kossuth University, Debrecen, Hungary, Private

Communication.

A. Grallert and J. Csikai, Institute of Experimental

Physics, Kossuth University, Debrecen, Hungary, Private

Communication.

"Chart of the Nuclides", W. Seelmann Eggebert, G.

Pfenning, H. Miinzel and H. Klewe Nebenius, Nov. 1981.

J. Csikai; Some Results on The Determinations of Helium

Production Cross-Sections, IAEA Consultants Meeting on

Improvement of Measurements Theoretical Computations and

218

Evaluations of Neutron Induced Helium Production Cross-

Sections, Debrecen, Hungary, Nov. 1992.

22- "Handbook On Nuclear Activation Cross-Sections", The

International Atomic Energy Agency, Technical Reports

Series No.156, p(91-115), Vienna 1974.

219

CHAPTER SIX

INVESTIGATIONS ON THE SYSTEMATICS OF (n,a) AND (nfp)

REACTIONS CROSS-SECTIONS AT 14.6 MEV NEUTRONS

Cross-sections of (n,p), (n,a) and (n,2n) reactions have

been measured by the activation method for a number of

elements and isotopes around 14 MeV neutron energy [1-3]. The

effect of (N-Z)/A asymmetry parameter as well as isotopic,

isotonic and odd-even properties of nuclei on the cross-

sections were observed by several authors [3-4]. The precise

knowledge of the different systematics has a great importance

in the estimation of the unknown data and in the adoption of

appropriate cross-section among the discrepant experimental

values. The accuracy of the mean neutron energy (« 20 KeV)

and the energy resolution (« 100 KeV) of D-T neutrons around

14 MeV rendered it possible to determine precise data for

absolute normalization of the measured and calculated

excitation functions. The main trends observed in the cross-

sections around 14 MeV neutron energy have been summarized in

reference [3]. A strong (N-Z)/A =s dependence was found in

the different reaction cross-sections.

The experimental data could be well approximated by the

following form of empirical formula proposed by Levkovsky

[4]:

220

a(n,x)= c a N E exp(-a(N-Z)/A) (6.1)

where a«g is the nonelastic cross-section, c and a are

fitting parameters (which are different for the a(n,p) and

a(n,a) data).

I In spite of the improved methods and more precise decay

parameters used for the determination of the cross-sections,

the existing data are still incomplete and often discrepant

around 14 MeV. Recently, Cheng and Smith [5] have given a

list of 83 activation reactions whose cross-sections are

insufficiently known. The spread is significant both in the

old and new data for (n,p) and (n,a) reactions [3,6].

Investigations were done in this work to improve the accuracy

of the data as well as to check on the behaviour of the

different (N-Z)/A parameter trends.

6-1 Experimental Procedure:-

High purity samples (from Goodfellow Co.) of 10x15 mm2

rectangular shape and 0.06-0.8 g/cm thickness were

irradiated, at angle 0° relative to the deuteron beam, with

14-6 MeV neutrons, produced by the neutron generator. The

neutron fluence and energy were determined via the

27Al(n,a)24Na, 93Nb(n,2n)92mNb and 90Zr(n,2n)89m+9Zr

reactions. Using known cross-sections from references

[7,8,12]. The samples were sandwiched between two Nb and Al

fluence monitor foils as shown in Fig[6-1]. To get relatively

high constant neutron flux, an off-centered rotating T-target

221

neutron flux Nb V Al Al Zr Nb101 101 102 103 101 104

Al101

IIITi Fe Nb Nb Mo Al101 101 102 103 101 104

Fig[6-1] The geometrical arrangement of samples irradiation

222

as used. The irradiation time used was 17.3667 hours. The

elative change of flux in time was monitored by means of BF~

ong-counter. The readings of the long-counter were taken

very 15 mins and are shown in Table[6-1]. The neutron

enerator high voltage used was 175 KV and the target current

as 150 fih. The activities of the samples were measured by

PGe detector. The detector efficiency is given by the

ormula f 9]:

e(E,R) = e(E) C(R) (6.2)

'here E is the photopeak energy in KeV, C(R) is the

:orrection for the efficiency due to the distance R from the

letector and R is the sample distance from the detector plus

:he sample thickness. C(R) is defined as:

C(R) = A/(d+R)2 (6.3)

/here

R = (11.25 + sample thickness) mm (6.4)

["he efficiency e(E) of the HPGe detector is given by the

aquation [9]:

A2lnE + A3ln2E + A4ln

3E (6.5)

223

Table [6-1]: The BF3 long-counter readings

timemins

153045607590105120135150165180195210225240255270285300315330345360375390405420435450465480495510525540555570585600615630645660675690705

BFreadings

3547933562348493480532955334613437831957311263508429332274123306534543352353511635283348093505736128343373649036176339373332334337336911671032989321523275031889325113261632518318253088530268306263002230083299432931118992286692808427622

timemins

720735750765780795810825840855870885900915930945960975990100510201035

BF_readings

27626242332724327469279732701526621263412495025504244062508117736258102432723254230672379324070236052249922876

\

224

For 50 KeV < E < 250 KeV the parameters are A =1073.3776,

d == 22.0577, A1 = -508.4741, A2 = 306.2717, A3 = -60.5834 and

A4 = 4.0065.

For 250 KeV < E < 2500 KeV the parameters are A =

1089.1132, d = 22.4317, A. = 11.7791, A_ = -2.4032, A- =_L 4L o

0.1042 and A. = 0.4

The total-to-peak ratio is given by the formula [9]:

In(total/peak) = -3.18431 + 0.79539 lnET(KeV) (6.6)

For the analysis of the spectra the GAMANAL code was

used [10]. The self-absorption correction factors for the

given geometries and gamma energies were calculated using the

formula (4.12). The reactions to be investigated and the

nuclear data accepted for the evaluation of the cross-

sections are given in Table [6-2] [11].

The reactions used for neutron fluence and energy

determination and the relevant nuclear data accepted for the

evaluation are shown in Table [6-3] [11].

6-2 Energy Determination of Neutrons using Zr(n,2n) m ^ Z r

Reaction:-

The samples used for cross-section determination were

fixed at angle 0° relative to the incident deuteron beam. To

check the energy of neutrons that strike the samples the

Zr(n,2n) m ^Zr reaction of well known excitation function

225

Table [6-2]:Nuclear data used for cross-section determination

reaction

50Ti(n,a)47Ca

51V(n/a)48Sc

51V(n,na)47Sc

D4Fe(n,a)D±Cr

90Zr(n,a)87mSr

94Zr(n,a)91Sr

92Mo(n,a)89Zr

98Mo(n,a)95Zr

100Mo(n,a)97Zr

48Ti(n,p)48Sc

54Fe(n,p)54Mn

90Zr(n,p)90inY

91Zr(n/P)91mY

y2Zr(n,p)y^Y

94Zr(n,p)94Y

92Mo(n,p)92mNb

95Mo(n/P)95mNb

half-life

4.536 d

1.821 d

3.341 d

27.7 d

2.81 h

9.52 h

3.268 d

64.02 d

16.9 h

1.821 d

312.2 d

3.19 h

49.71 m

3.54 h

18.7 m

10.15 d

3.61 d

Ef (KeV)

1297.06

175.36983.051037.51312.05

159.38

320.08

388.4

749.81024.3

909.2

724.2756.73

743.33

175.36983.51037.51312.05

834.83

202.47479.53

555.6

448.5561.1934.5

918.741138.9

934.44

235.68

Jr %

74.9

7.4710097.5100

68

10.08

82.26

23.633.4

99.87

44.154.5

94.83

7.4710097.5100

99.97

96.690.7

100

2.332.4313.92

56.36

99

24.9

abunda-nce %

5.2

99.75

99.75

5.8

51.5

17.4

14.8

24.1

9.6

73.7

5.8

51.5

11.2

17.1

17.4

14.8

15.9

226

:ont. Table [6-2]

reaction

96Mo(n,p)96Nb

98Mo(n,p)98mNb

half-life

23.35 h

51.3 m

E (KeV)

568.84778.2460.051091.331200.19810.24849.95

335.2722.5787.2

T

56.996.828.648.719.91020.6

10.77193

abunda-nce %

16.7

24.1

227

Table [6-3]: Nuclear data of the normalization standards

reaction

^/Al(n,a)^*Na

93Nb(n,2n)92mNb9O-7W~ O n \89m+g7 v .

half-life

15.03

10.14

78.43

h

d

h

Ef (KeV)

1368.6

934.5

909.5

1 0 0

9 9 .

9 9 .

%

2

0 1

abunda-nce %

100

100

51.5

228

around 14 MeV was used.

The cross-section of Zr(n,2n) m gZr was measured

93 92using Nb(n,2n) Nb reaction as standard. The cross-section

93of Nb(n,2n) reaction is constant around 14 MeV and it is

equal to 460±5 mb [12]. Thus the cross-section of

Zr(n,2n) gZr could be measured by measuring the cross-

section ratio a /a . The foils used for measurements were

Zr101 anc* N^103 a s s n o w n in Fig[6-1]. The results obtained

are shown in Table [6-4]. The flux correction to the Zr-01

foil due to the attenuation of neutrons by Nb--3 is 1.0505.

Using equation (5.1) and taking the values from Table

[6-4], the cross-section ratio a r/a was found to be

1.6596. That means the cross-section of 90Zr(n, 2n)89ltl+gZr is

763.433 mb, while in reference [7] the cross-section of this

reaction at 14.6 MeV neutrons was 763.21 mb. Comparing the

two results one can say that the energy of the neutrons that

was used to irradiate the samples would be 14.6±0.02 MeV.

6-3 Results of Foils used as Fluence Monitor:-

The foils used as fluence monitors were Al 1 0 2, A 1 1 Q 3 and

Nb103* T h e c a s c a d e o f energies 1368 KeV and 2754 KeV in the27 24

Al(n,a) Na reaction is shown in Fig[5-7], The results

obtained for these monitors are shown in Table [6-5]. The

atomic weight of 27A1 is 26.98154 and of 93Nb is 92.9064

[13]. A typical spectrum of A 1 1 Q 2 is shown in Fig[6-2].

229

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6-4 The (n,a) Reaction Cross-Section Results:-

The data for the (n,a) cross-section measurements are

summarized in Table [6-6]. The different corrections needed

for the measurements and calculations were done as shown in

Chapters 4 and 5.

The typical spectra of Fe, V, Zr and Mo are shown in

Figs [6-3], [6-4], [6-5] and [6-6], respectively.27 24Using the cross-section of Al(n,a) Na from reference

[14], which is 117.94 mb, the results of the (n,a) cross-

sections under evaluation have been determined and are shown

in Table [6-7].

For statistical and dead-time error calculations the

uncertainties of the peak area and pulser peak area were

used, respectively. The error of the HPGe detector efficiency

used was 1% [9]. The errors of the half-lives and gamma

intensities were taken from reference [11].

6-5 The (n,p) Reaction Cross-Section Results:-

The data for the (n,p) cross-section measurements are

summarized in Table [6-8]. The different corrections needed

were done as shown in Chapter 4.

The cascade schemes of 9 0 mY, 92Y, 94Y, 96Nb and 98mNb

are shown in Figs [6-7], [6-8], [6-9], [6-10] and [6-11],

respectively.

Using the known 93Nb(n,2n)92raNb reaction cross-section27 24

of 460 mb [12] and the known Al(n,a) Na reaction

233

Table [6-6]: Data for the (n,a) cross-section measurements

reaction

54Fe(n,a)51Cr

50Ti(n,a)47Ca

51V(n,a)48Sc

51V(n,na)47Sc

90Zr(n,a)87niSr

94Zr(n,a)91Sr

92Ho(n,a)89Zr

98Mo(n,a)95Zr

100Mo(n,a)97Zr

h

102.91

11.77

7.84

7.84

0.21

4.61

16.78

16.78

16.78

12

1.

3.

3.

0.

0.

5.

5.

5.

h

.61

33

88

88

69

75

89

89

89

sKeV

320

1297

983

159.

388.

749.

909

757

743

39

4

8

lr

10.2

77

100

68.5

82.26

23.6

99.01

54.6

92.8

atomicweight

55.847

47.900

50.940

50.940

91.220

91.220

95.940

95.940

95.940

I

0

0

0

0

0

0

0

0

0

nassgm

.60100

.37100

.46599

.46599

.50855

.50855

.73848

.73848

.73848

peakarea

21735

1741

612645

13735

49763

2230

84821

1416

14824

specificactivity

s

3490.5

3460.3

406484.0

8475.9

163477.2

8390.0

24511.0

393.9

8062.1

dead-timecorr.

ed

0.9910

0.9362

0.9743

0.9743

0.9980

0.9990

0.9463

0.9463

0.9463

self-abs.

0

0

0

0

0

0

0

0

0

980

977

969

976

953

980

.985

.983

.980

casca-decorr.

-

-

0.7916

-

-

-

-

-

efficien-cycorr.

£(E)

0.

0.

0.

0.

0.

0.

0.

0.

0.

036761

008395

010883

086560

029244

014830

011752

014410

014600

fluxvaria.corr.

S

529.642

3078.16

7054.37

4009.76

25406.8

20873.9

4109.53

237.608

15172.2

fluxcorr.dueatt.

0

0

0

0

0

0

0

0

0

915

773

836

836

929

929

.820

820

.820

moni-torfoilused

^ 1 0 2

A11 Q 2

^ 1 0 2

A1102

^ 1 0 3

^ 1 0 3

ftl103

^ 1 0 3

A1103

rfl

(N

I

<

(0

n

9OHi

3"

0)a

X}

09

I

01XI

o

OMi

3*(V

(A

3T3

^^

H-

3ow

X)n>nftl-t

9

Q

O

Ulto3)

Table [6-7]: Results of measured (n,a) reaction cross-

sections around 14.6 MeV

reacion

50Ti(n,a)47Ca

51V(n,a)48Sc

51V(n,na)47Sc

54Fe(n,a)51Cr

90Zr(n,a)87mSr

94Zr(n,a)91Sr

92Mo(n,a)89Zr

98Mo(n,a)95Zr

100Mo(n/a)97Zr

cross-section ratio

ox/aA1

0.07292

0.14414

0.000763

0.72920

0.03222

0.03985

0.22220

0.05003

0.02713

(n,a) cross-section

mb

8.6 ± 0.6

17 ± 1

0.09 ± 0.005

86 ± 5

3.8 ± 0.2

4.7 ± 0.3

26.2 ± 1.2

5.9 ± 0.3

3.2 ± 0.2

Table [6-8]: Data for the (n,p) cross-section measurements

reaction

92_ 92Tfo(n,p) Nb

54 54Fe(n,p) Mn

Zr(n,p) Y

9V,p)'4*92 92

Zr(n,p) y48m., ,48,,

Tl(n,p) Sc

95 95mMo(n,p) Nb

96 , , 96 -Mo(n,p) Nb

98 98mHo(n,p) Nb

H

h

16.78

102.91

4.60

0.21

0.21

0.21

81.83

16.78

16.78

0.93

5.

12

0.

0.

0.

0.

1C

5

5

0

h

89

.61

75

69

69

69

.57

89

89

53

KeV

934.

834.

479.

555.

918.

934

983

235

109

787

50

85

53

60

74

50

50

60

L.3

\

100

100

90.70

100

56.30

13.92

100

25

51

93.20

atomicweight

95.

55

91

91

91

91

47

95

95

95

94

85

22

22

22

22

90

94

94

.94

massgm

0

0

0

0

0

0

0

0

0

0

73848

60100

50855

50855

50855

.50855

37102

.73848

.73848

.73848

peakarea

88450

26347

58996

41452

2930

5659

1276382

33145

64506

5810

specificactivity

h

22714

3585.8

455235.5

186423.2

26181.7

18082.8

1330976.9

8909.3

28088.6

41597.8

dead-timecorr.

ed

0

0

0

0

0

0

0

0

0

0

9463

9795

9990

9960

9960

9960

9590

9463

9463

.9400

self-abs.

0

0

0

0

0

0

0

0

0

0

985

982

960

965

985

985

969

.951

.986

.984

casca-decorr.

c

0.8900

-

0.8435

-

0.8875

0.8517

0.7911

-

0.8785

0.7900

efficien-cy

corr.6(E)

0.

0.

0.

0.

0.

0.

0.

0

0

0

011570

012790

023004

019790

011766

011572

010883

055450

010027

013730

fluxvaria.corr.

S

-

47.4135

25492.5

23527.6

23056.3

25479.6

7054.66

3799.40

11534.0

23549.8

fluxcorr.dueatt.

0.820

0.915

0.929

0.929

0.929

0.929

0.773

0.820

0.820

0.820

moni-torfoilused

% 3

^102

U103

SB

^103

M103

U102

M103

M103

^103

sr

479.53 KeV

202.5 KeV

90

90 mFig[6-7] The cascade scheme of Y isotope

241

92

Pi6.5%

1.2%

2.3%

3.5%

86%

844.3(19%] KeV

561.1 KeV

448.5 KeV

934.5 KeV

Zr

92Fig[6-8] The cascade scheme of Y istope

242

5.3%

4.1%

40%

41%

1138.9[97%] KeV

550.9 KeV

918.8 KeV

94Zr

94Fig[6-9] The cascade scheme of Y isotope

243

p95.9%

568[57%J KeV

1091.3 KeV

778.22 KeV

96Mo

Fig[6-10J The cascade scheme of Nb isotope

244

98Nb

P T1 %

5%

833 KeV

„ 722 KeV

787 KeV

98Mo

98Fig[6-11] The cascade scheme of Nb isotope

245

cross-section of 117.94 mb [14], the studied (n,p) reaction

cross-sections have been determined and are shown in Table

[6-9].

5-6 Discussion:-

The results for the (n,a) cross-section measurements in

this work and in reference [17], are summarized in Table [6-

10] together with the data of Forrest and Ikeda [6,15]. These

results are also demonstrated in Fig[6-12] as function of the

parameter (N-Z)/A. The data adopted by Forrest [6] and

measured by Ikeda et al.[15] are given for comparison.

It was found that the simple formula represented by

equation (6.1) can be used to estimate the a(n,.a) data. The

expression for the calculation of aNE data deduced from a

semiclassical optical model can be found in reference [16].

The values of C and "a" parameters obtained from the fitting,

for s> 0.03, are summarized in Table [6-11] with a(n,a) given

in mb.

According to the present results the following simple

expression is also suitable to approximate the experimental

data:

o(n,a) = aQ exp(-aQ s) (6.7)

where s= (N-Z)/A, and using the parameter values given in

Table [6-11]. The pre-exponential terms are in agreement

246

Table [6-9]: Results of measured (n,p) reaction cross-sections around 14.6 MeV

reacion

48Ti(n,p)48Sc

54Fe(n,p)54Mn90Zr(n,p)90mY

9 1Zr(n / P)9 1 i nY

92Zr(n,p)92Y

94Zr(n,p)94Y

92Mo(n,P)92inNb

95Mo(n /P)95lnNb96Mo(n,p)96Nb98Mo(n /P)98inNb

cross-section ratio

aX /aAl /Nb

0.5681

2.6200

0.1128

0.2035

0.1696

0.0619

0.1540

0.0695

0.2120

0.0449

(n,p)

67

cross-section

mb

± 4

309 ±

1 3

2 4

2 0

7 .

7 0

8 .

2 5

5 .

. 3 ±

± 1

± 1

3 ±

. 8 ±

2 ±

± 1

20 ±

1 7

0 . 7

. 2

. 0

0 . 8

4 . 2

0 . 6

. 3

0 . 2 4

247

Table [6-10]: Recent measured and evaluated data for some(n,a) reaction cross-section around 14.6 MeV

reaction

50Ti(n,a)47Ca

51V(n,a)48Sc

51V(n,na)47Sc

54Fe(n,a)51Cr

90Zr(n,a)87mSr

94Zr(n,a)91Sr

92Mo(n,a)89Zr

98Mo(n/a)95Zr

100Mo(n,a)97Zr

45Sc(n,a)42K

54Cr(n/a)51Ti

55Mn(n,a)52Cr

78Se(n,a)75mGe

59Co(n,a)56Mn

78Se(n,a)75Ge

80Se(n,a)77mGe

80Se(n,a)77Ge

89Y(n,a)86Rb

114Cd(n,a)lllmPd

115In(n,a)112Ag

118Sn(n,a)115<?cd

(N-Z)/A

0.12000

0.09804

0.03704

0.11111

0.14894

0.08696

0.14290

0.16000

0.06700

0.11111

0.09100

0.12800

0.08500

0.12800

0.15000

0.15000

0.12400

0.15800

0.14800

0.15300

Forresta(mb)[6]

8.75±0.80

16.15±0.75

88.5±6.0

4.3±0.6

27.3±1.5

5.80±0.35

3.19±0.25

56±3

12.6±1.5

27.5±4

30±l

5.5±2

17±6

5.5±0.5

2.4±0.3

Ikeda et.al. a(mb)

[15]

9.

16

84

3.

4.

24

6.

2.

53

31±0 .78

•94±0.87

.5±6

65±0

90±0

.5±1

45±0

81±0

.3±4

.0

.22

.42

.2

.49

.20

.3

presentand [17]a(mb)

present

8.6±0.6

17±1

0.090±0.005

86.0±5

3.8±0.2

4.7±0.3

26.2±1.2

5.9±0.3

3.2±0.2

Ref[17]

53.7±2.6

10.8±2.1

22.012.1

4.5+0.7

31±1

6.4+1.2

1.110.2

3.6+0.3

5.4+0.6

0.30+0.03

2.3+0.2

0.9010.08

248

cont. Table [6-10]:

reaction

12OSn(n,a)117mCd

12OSn(nfa)1179cd

142Nd(n,a)139Ce

144Nd(n,a)141Ce

146Nd(n,a)143Ce

184W(nf«)181Hf

186W(n,a)183Hf

203Tl(n,a)200gAu

206Pb(n,a)203Hg

(N-Z)/A=s

0.16700

0.16700

0.15500

0.16700

0.17800

0.19600

0.20400

0.20200

0.20400

Forresta(mb)[6]

6.8+1.5

4.711.5

3.1+0.5

1.1510.15

0.5510.07

211

Ikeda et.al. a(mb)

[15]

0.183+0.07

0.23+0.08

0.60+0.11

presentand [17]a(mb)

0.2110.09

0.2610.03

5.5+0.4

4.010.3

3.510.3

0.8510.09

0.5410.05

0.37+0.06

0.5710.04

2 4 9

1?

10

0

10-j

• presentV Forrest

O Ikeda et al.calc. (eq. 6

I J

0.05i L.

0.10 0.15 0.20(N-Z)/A

Fig[6-12] Dependence of (n,a) cross-sections on (N-Z)/A asymmetry parameter

Table [6-11]: Fitting parameters values deduced from datasets given by different Authors for (n,a)reaction

para-meter

C

a

°0ao

Forrest

0.3296±0

32.90±0.

316.7±38

28.50±0.

[6]

.0390

78

.9

78

Ikedanet. al.L5]

0.386810.0700

33.9±1 5

363.3±56.7

29.9±1 3

present

0.3302±0.

33.6±1.7

311.6±71.

29.211.6

and [17]

0780

0

251

within about 15% while the values of the slopes agree within

the limits of errors independently of the investigated

nuclei. As can be seen in Fig[6-12], there is a relatively

large spread in the (n,a) cross-sections around the straight-ft C\ "} C\ f\

line. For example, in the case of Se and Pb the measured

data in reference [17] are consistent with the recommended

trend while the data obtained for the Nd isotopes are higher,in agreement with those adopted by Forrest. The o(n,a) for120

Sn is in agreement with the data measured by Ikeda et al.

[8] but deviates significantly from the recommended straight

line obtained by equation (6.7). The a(n,a) data as a

function of "s" cover a large interval for the ^ f ^ 0 / iUUMo

isotopes. These data are in good agreement with the

predictions of equation (6.1) and (6.7).

For comparison, the Forrest [6] (n,a) cross-sections

adopted data and the calculated (n,a) cross-sections using

equation (6.7) are shown in Table [6-12].

If the ratio of ffadopted/acalculated is plotted against

the s value the graph in Fig[6-13] is obtained. In this graphmost of the cross-sections ratios are around unity within

80 203less than 30%. However, Se and Tl are far from unity.

Pashchenko et al. [18] have demonstrated the presence of

the odd-even effects in the (n,a) cross-sections by taking

into account the different reaction Q-values of each

252

Table [6-12]: The a(n,a) Forrest [6] adopted data and theresults of calculated data using equation (6.7)

the targetelement

44Ca

50Ti5 1v50Cr

54Cr

54Fe

55Mn

59Co

64Ni

68Zn

45Sc

48 T i

52Cr

56Fe

57Fe

58Fe

58Ni

60Ni

61Ni

62Ni

63CU

65Cu

N-Z/A=S

0.091

0.120

0.098

0.040

0.111

0.037

0.091

0.085

0.125

0.118

0.067

0.0833

0.077

0.0714

0.0878

0.103

0.035

0.067

0.082

0.097

0.079

0.108

Forrest'sadopted c.s.

mb[6]

28.611.5

8.75+0.80

16.15+0.75

90120

12.611.5

88.516.0

27.5+4.0

30.111.0

3.711.5

10.311.8

5613

3118

3318

46+4

3313

20+2

120115

70110

45+6

21.5+3.0

40.7+2.5

13.7+4.0

calculatedc.s. usingeq.(6.7)

mb

21.86

9.37

17.82

96.904

12.19

105.78

21.86

26.04

8.1

9.94

44.05

27.37

32.9

38.74

24

15.4

112.14

44.05

28.43

18.344

31.03

13.31

aadoptedQ

1.309

0.930

0.910

0.930

1.030

0.840

1.260

1.160

0.460

1.040

1.270

1.130

1.003

1.190

1.370

1.300

1.070

1.590

1.580

1.170

1.310

1.030

253

cont. Table [6-12]:

the targetelement

68Zn

74Ce

75As

78Se

80Se

85Rb

89 y

90Zr

94Zr

93Nb

92Mo

94Mo

95Mo

96MO

97MO

98Mo

100Mo

107Ag

109Ag

115In

126Te

138Ba

N-Z/A=s

0.118

0.135

0.120

0.128

0.150

0.129

0.124

0.111

0.149

0.118

0.087

0.106

0.116

0.125

0.134

0.143

0.160

0.122

0.138

0.148

0.175

0.188

Forrest'sadopted c.s.

mb[6]

10.3±1.8

6.1±1.0

11.Oil.5

5.512.0

17.016.0

6.6510.25

5.510.5

1013

4.310.6

9.50+0.75

27.3+1.5

17.5+4.0

13.512.0

1012

7.5+2.0

5.8010.35

3.1910.25

5.513.0

7 + 3

2.4+0.3

2.3010.25

2.5310.20

calculatedc.s. usingeq.(6.7)

rob

9.93

6.05

9.37

7.42

3.90

7.21

8.33

12.19

4.020

9.93

24.56

14.11

10.53

8.10

6.23

4.79

2.92

8.84

5.54

4.14

1.88

1.29

aadopted

1.040

1.010

1.170

0.740

4.360

0.922

0.660

0.820

1.070

0.960

1.110

1.240

1.280

1.230

1.200

1.210

1.090

0.620

1.260

0.580

1.220

1.970

254

cont. Table [6-12]:

the targetelement

139La

140Ce

1 4 2Ce

142Nd

144Nd

146Nd

148Nd

150Sm

152Sm

154Sm

151Eu

1 5 3Eu

156Gd

158Gd

1 5 9Tb

162Dy

164Dy

1 6 5Ho

168Er

170Er

169Tm

1 7 2Yb

N-Z/A=s

0.180

0.171

0.183

0.155

0.167

0.178

0.189

0.173

0.184

0.195

0.166

0.177

0.180

0.190

0.182

0.185

0.195

0.188

0.191

0.200

0.183

0.186

Forrest'sadopted c.s.

mb[6]

2.010.3

4.612.0

3.0+0.6

6.811.5

4.7+1.5

3.110.5

2.410.5

3.410.6

2.110.5

0.9810.10

4.210.5

2.210.4

3.1+1.0

1.22+0.38

2.510.6

2.0010.25

1.2410.14

1.25+0.35

2.310.5

0.6510.05

3.0+1.5

1.8010.35

calculatedc.s. usingeq.(6.7)

mb

1.63

2.11

1.49

3.37

2.38

1.72

1.25

1.99

1.45

1.05

2.45

1.78

1.63

1.21

1.53

1.41

1.05

1.29

1.18

0.91

1.49

1.36

aadopted

1.230

2.180

2.010

2.020

1.980

1.800

1.920

1.700

1.450

0.930

1.720

1.240

1.910

1.010

1.630

1.420

1.180

0.970

1.950

0.720

2.010

1.320

255

cont. Table [6-12]

the targetelement

174Yb

176Yb

175LU

176LU

178Hf

180Hf

181Ta

1 9 00s

197Au

203T1

206pb

27A1

184W

186W

N-Z/A=S

0.195

0.205

0.189

0.193

0.191

0.200

0.193

0.200

0.198

0.202

0.204

0.037

0.196

0.204

Forrest'sadopted c.s.

mb[6]

1.26+0.20

0.7±0.3

1.3110.20

1.110.2

1.610.3

0.8010.15

1.110.3

0.8210.08

0.510.1

2.211.0

0.737

113

0.848

0.644

calculatedc.s. usingeq.(6.7)

mb

1.05

0.78

1.25

1.11

1.18

0.91

1.11

0.91

0.96

0.86

0.81

105

1.02

0.81

aadopted

rsels-

1.200

0.890

1.050

0.990

1.360

0.880

0.990

0.910

0.520

2.570

0.910

1.070

0.830

0.800

256

0.00.0 0.20.1

(N-Z)/A

Fig[6—13] Ratio of adopted to calculated cross-sections using

Forrest[6] and eq.(6.7).

nuclide. Considering the present status of the data it is

recommended to predict the unknown cross-sections by using

equation (6.7) with the parameters deduced from the Forrest's

adopted values, especially for reactions in which long-lived

or stable nuclides are produced. In addition, studies on

isotopic effects in a(n,a) at a given Z were carried out by

different investigators. The data from Qaim [1], Forrest [6],

Ikeda et al. [15] and the present work are shown in Table

[6-13], where in the calculated data equation (6.7) and the

parameters deduced from Forrest data were used. The data of

Table [6-13] are demonstrated in Fig[6-14]. As can be seen in

Fig[6-14] the a(n,a) values as a function of the mass number

A show a linear dependence in semilog plot for a given

element and these straight lines are almost parallel to each

other. In some cases the measured and calculated data using

equation (6.7) deviate significantly. Fig[6-14] clearly

indicates that the observation of any fine structure requires

more precise measurements, therefore it is recommended to

further refine the a(n,a) data and to improve the

systematics.

The measured cross-section values for (n,p) reaction and

the measured data in reference [17], are summarized in Table

[6-14] and demonstrated in Fig[6-15], as a function of

(N-Z)/A, together with the results of Forrest [6] and Ikeda

et al.[15] for comparison.

The fitting parameter values in equation (6.1) and (6.7)

258

Table [6-13]: The (n,a) cross-section data for differentisotopes at a given Z

massno.

A

50

54

52

54

56

57

58

58

64

60

61

62

63

65

90

94

92

94

95

96

97

98

targ-etelem-ent

Cr

Cr

Cr

Fe

Fe

Fe

Fe

Ni

Ni

Ni

Ni

Ni

Cu

Cu

Zr

Zr

Mo

Mo

Mo

Mo

Mo

Mo

Z

24

24

24

26

26

26

26

28

28

28

28

28

29

29

40

40

42

42

42

42

42

42

Forrest[6]

a(mb)

90

12.6

33

88.5

46

33

20

120

3.7

70

45

21.5

40.7

13.7

10

4.3

27.3

17.5

13.5

10

7.5

5.8

Qaim[1]

a(rab)

25

5.5

Ikeda[15]

a(mb)

84.5

3.65

4.9

24.5

6.45

present

a(mb)

10.8

86

3.8

4.7

26.2

5.9

calculated

a(mb)

101.3

13.4

35.3

110.3

41.4

25.9

16.8

116.8

8.9

46.9

30.6

20

33.3

14.6

13.4

4.53

26.5

15.44

11.6

8.9

7

5.4

259

cont. Table [6-13]

massno.

A

100

142

144

146

148

targ-etelem-ent

Mo

Nd

Nd

Nd

Nd

Z

42

60

60

60

60

Forrest[6]

cr(mb)

3.19

6.8

4.7

3.1

2.4

Qaim[1]

a(mb)

2.8

Ikeda[15]

a(mb)

2.81

84.5

present

a(mb)

3.2

5.5

4

calculated

a(mb)

3.3

3.8

2.71

2

1.5

260

10

y n - r r p T r i " [ i i n*]"TT"n~prri~r[TTTTyT'i~n"p"n~rp"i~in~[-TT rryT r-T""r"T"r-T r

Cr

Mo

Nd

nNi

i Q Lj_U-±i-L.i-i . iJ X L I l-Ll.-i.-L J_LxX-J I 1 jq..i-xl-l.-1-J. iJ . L_LJ.1.I.1J_J..L 1 L 1 J_i_l ±0-1.1.1 X^L.J.1 1 I. L 1. l_i ±_ l . l ± / /X L_. _L ._[ . . J -1 _ i __ i

40 45 50 55 60 65 70 75 80 85 90 95 100105110 150 160

AFig[6—14] The isotopic effect in the (n,a) cross sections , using the data from Qaim [l

Forrest [6], Ikeda et al. [15] Ref. [17] and present work with solid lineecalculated by eq. (6.7) and Forrests adopted data.

10, \

Table [6-14]: Recent measured and evaluated data for some(n,p) reaction cross-sections at 14.6 MeV

reaction

48Ti(n,p)48Sc

54Fe(n,p)54Mn

90Zr(n,p)90mY

91Zr(n/P)91mY

92Zr(n,p)92Y

94Zr(n/P)94Y

92Mo(n,p)92inNb

95Mo(n,p)95mNb

96Mo(n,p)96Nb

98Mo(n,P)98mNb

74Se(n,p)74As

76Se(n/P)76As

78Se(n,p)78As

11OCd(n,P)11OmAg

"W.P)111**112Cd(n,p)112Ag

113Cd(n,p)113mAg

115In(n,p)1159cd

115In(n,P)115raCd

116Sn(n,P)116mIn

117Sn(n,p)117In

118Sn(n,p)118Cd

(N-Z)/A=s

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

.08333

.0370

.1111

.1210

.1304

.1490

.0870

.1160

.1250

.1430

.0811

.1053

.1280

.1270

.1350

.1430

.1504

.1480

.1480

.1380

.1453

.1530

Forresta(mb)[6]

67±8

315±10

19.2±2.0

10±l

21±2

135±15

70±10

18±4

50±15

16±3

13 + 2

7±2

Ikeda et.al. a(mb)

[15]

60 .4±2.9

287±13

13

18

22

8.

63

7.

24

6.

10

14

.28±0.89

.3±1.0

.2±2.3

91+0.72

•6±3.1

79±0.74

•0±1.2

25±0.40

.68±0.83

.01±1.18

presentand [17]a(mb)

Present:67±4

309±17

13.3±0.7

24.0±1.2

20±l

7.3±0.8

70.8±4.2

8.2±0.6

25.0±1.3

5.20±0.24Ref[17]:112±7

49±3

19.011.1

10.811.4

29.012.1

16.011.2

17+1

4.0010.25

7.4012.95

10.810.7

20.011.2

6.2010.46

262

cont. Table [6-14]:

reaction

142Nd(n,p)142Pr

146Nd(n,P)146Pr

182W(n,P)182Ta

183W(n/P)183Ta

184W(n,P)184Ta

(N-Z)/A=s

0.1550

0.1780

0.1870

0.1910

0.1960

Forresta(mb)[6]

13.8±1.1

4.5±0.7

5.9±0.5

4.1±0.5

3.0±0.4

Ikeda et.al. a(mb)

[15]

presentand [17]a(mb)

13.6±0.9

4.110.4

6.5±0.5

5.0±0.4

3.2±0.2

263

10'

a TO

10

D present & Ref.[17]V Forrest

0 Ikeda et al.

calc. (eq. 6.7)

0.05 0.200.10 0.15

(N-Z)/AFig [6—15] Dependence of (n,p) cross section on (N —Z)/A

deduced from the remeasured and adopted (n,p) reaction cross-

sections are summarized in Table [6-15]. The slopes of the

a(n,p) Vs s functions are the same within the limits of

errors, however, the magnitudes of these cross-sections

deviate significantly. The remeasured data in this work

support the adopted values of Forrest, however, both data

sets are higher up to about 30% in the whole (N-Z)/A range

than those obtained by Ikeda et al. [15]. It is difficult to

explain this discrepancy since in the a(n,ot) data excellent

agreement was achieved, with the (n,p) values obtained for

the same nuclei in the two experiments. Similarly to the

(n,a) cross-sections, more data of high precision are

required for (n,p) cross-sections to deduce any fine

structures and to improve the systematics.

It is worthwhile to mention that the shapes of the

a(n,p)-s functions for isotopes of different elements are not

similar to those obtained for the (n,a) reactions. The

measured and calculated a(n,p) data for various isotopes are

shown in Table [6-16]. The isotopic effect is also

demonstrated in Fig[6-16], The results of the calculations

using equation (6.7), with the parameter values deduced from

the measured data and data in reference [17] show good

agreement with recent data. The equation (6.7) may thus be

used, to a good approximation, for the estimate of the

unknown (n,p) cross-sections.

265

Table [6-15]: Fitting parameter values deduced from data setsgiven by different authors for (n,p) reactions

parameter

C

a

aoao

Forrest

0.892±0.

33.02±0.

8691100

29.03±0.

[6]

093

69

77

Ikeda et[15]

0.62610.

31.9411.

648196

28.5411.

al.

074

22

56

present andreference [17]

0.83310.170

32.211.4

852+200

28.011.6

266

Table [6-16]: Measured (n,p) cross-sections and calculatedvalues using equation (6.7) and the parametersdeduced from present measurements and reference[17] for some isotopes

reaction

74Se(n,p)74As

76Se(n,p)76As

78Se(n,p)78As

90Zr(n,P)90mY

91Zr(n,P)91InY

y^Zr(n,p)y^Y

94Zr(n/P)94Y

92Mo(n,p)92mNb

95Mo(n,p)95inNb

96Mo(n,p)96Nb

98Mo(n,p)98raNb

11OCd(n/P)11OmAg

111Cd(n,p)111Ag

112Cd(n,p)112Ag

113Cd(n,P)113mAg

116Sn(n/P)116roIn

117Sn(n/P)117In

Sn(n,p) In

142Nd(n,p)142Pr

146Nd(n,p)146Pr

182W(n,P)182Ta

(N-Z)/A=s

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0811

1053

1280

1111

1210

1304

1490

0870

1160

1250

1430

1270

1350

1430

1504

1380

1453

1530

1550

1780

1870

measured a(n,p)present andreference [17]

11217

49±3

19.0+1.1

13.3±0.7

24.0+1.2

20±l

7.3±0.8

70.814.2

8.2+0.6

25.011.3

5.2010.24

10.811.4

29.0+2.1

16.0+1.2

17+1

10.8+0.7

20.011.2

6.20+0.46

13.610.9

4.1+0.4

6.5+0.5

calculateda(n,p) usingequation (6.7)

88

44.

23.

38

28.

22.

13.

74.

33.

25.

15.

24.

19.

15.

12.

17.

14.

11.

11.

5.8

4.5

67

66

8

1

1

6

1

7

5

3

5

5

6

9

6

8

1

267

cont. Table [6-16]:

reaction

183W(n,p)183Ta

184W(n,p)

184Ta

(N-Z)/A=s

0.1910

0.1960

measured a(n,p)present andreference [17]

5.0±0.4

3.2±0.2

calculateda(n,p) usingequation (6.7)

4.1

3.5

268

Hi10

<X Se

—L- » - -L--L -

"• r

o

Nd

A

Aw

0.08 0.10 0.18J J I L L.

0.200.12 0.14 0.16

(N-Z)/AFig [6-16] Isotopic effect in (n,p) cross sections measured in this work

and Ref. [17], with dotted line calculated by eq (6.7) using the

parameter's deduced from the present data.

REFERENCES

1- "Handbook of Spectroscopy11, S.M. Qaim, Vol. Ill, CRC

Press, Inc. Boca Raton, Florida, (1981), P.141.

2- "Neutron Cross-Sections", V. Mclane, C.L. Dunford and P.F.

Rose, Vol. 2, Academic Press, Inc., Boston (1988).

3- "Handbook of Fast Neutron Generators", J. Csikai, CRC

Press, Inc. Florida (1987), Vol. II.

4- V.N. Levkovsky, Eksp. Teor. Fiz. 45(1963), P.305.

5- "Nuclear Data for Science and Technology", E.T. Cheng and

D.L. Smith, S.M. Qaim (Ed.), Springer-Verlag Berlin (1992)

P.273.

6- R.A. Forrest, Systematics of neutron-induced threshold

reactions with charged products at about 14.5 MeV, AERE

Report 12419 (1986).

7- J. Csikai, Cs.M. Buczko, R. Pepelnik and H.M. Agrawal,

Activation Cross-Sections Related to Nuclear Heating of

High T Superconductors, Ann. nucl. Energy. Vol. 18, No.o

1, (1991) pl-4.

8- "ENDF Pre-Processing Codes", D.E. Cullen, IAEA, Nuclear

Data Section, 1991.

9- F. Cserpak and J. Csikai, Institute of Experimental

Physics, Debrecen, (private communication).

10- Nuclear Analysis Software, GANAAS, part 2, IAEA, Vienna,

1991.

11- "Table of Isotopes", A.A. Shihab-Eldin, L.J. Jardine,

270

J.K. Tuli and A.B. Buyrn, John Wiley and Sons, INC.

Toronto (1978).

12- T.B. Ryves, A simultaneous evaluation of some important

cross-sections at 14.7 MeV, Report EUR 11912-EN (in

press).

13- "Chart of the Nuclides", W. Seelmann, G. Pfenning, H.

Munzel and H. Klewe, Kernforschungszentrum, Karlsruhe,

1989.

14- "ENDF, Pre-Pocessing Codes", D.E. Cullen, IAEA, Nuclear

Data Section 1989.

15- Y. Ikeda, Ch. Konno, K. Oishi, T. Nakamura, H. Miyade, K.

Kawade, H. Yamamoto and T. Katoh, JAERI 1312 ( Japan,

1988).

16- A.B. Pashchenko, O.T. Grudzevich and A.V. Zelenetsky,

IAEA RCM-I on Helium Production Data, 17-19 Nov. 1992.

17- A. Grallert, J. Csikai, Cs.M. Buczko and I. Shaddad,

Investigations On the Systematics In (n,a) Cross-Sections

At 14.6 MeV, INDC(NDS)-286, 131, IAEA, Nov. 1993.

18- M. Wagner, H. Vonach, A. Palvik, B. Stromaier, S. Tagesen

and Martinez Rio, Physics Data, Fachinformationszentrum,

Karlsruhe, Nr. 13-15, 1990.

271