379

V, /27/

A STUDY OF L-SHELL X-RAY PRODUCTION CROSS SECTIONS

DUE TO 1H, He, and 7 Li ION BOMBARDMENT OF1 2 3

SELECTED THIN RARE EARTH AND 82Pb TARGETS

DISSERTATION

Presented to the Graduate Council of the

North Texas State University in Partial

Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

By

Glenn Michael Light

Denton, Texas

May, 1978

Light, Glenn M., A Study of L-Shell XRay Production

Cross Sections Due to 1H 4He, and Li Ton Bombardment o f___ ____ ____1-'2- -3---_

Selected Thin Rare Earth and 8 2Pb Targets. Doctor of

Philosophy (Physics), May 1978, 106 pp., 3 tables, 19 figures,

bibliography, 90 titles.

Thin target L-Shell x-ray production cross sections

for protons incident on 6 2Sm and 70Yb in the energy range

of 0.3 to 2.4 MeV/amu, alpha particles incident on 62Sm,

70Yb, and 82Pb in the energy range of 0.15 to 4.8 MeV/amu,

and lithium ions incident on 58Ce, 60Nd, 62Sm, 66Dy, 67Ho,

70Yb, and 82Pb in the energy range of 0.8 to 4.4 MeV/amu

have been measured. The cross section data have been

compared to the planewave Born approximation (PWBA) and

the PWBA modified to include binding energy and Coulomb

deflection effects. The La,2 x-ray production cross

sections are best represented by the PWBA modified to

include both the binding energy and Coulomb deflection

effects (PWBA-BC) over the entire incident ion, incident

energy, and target ranges studied. However, the Ly1 and

LY2,3,(6) x-ray production cross sections are best repre-

sented by the PWBA except at the lower ion energies, where

both the PWBA and PWBA-BC are in disagreement with the data.

The comparison of La 1 2 /LY2 ,3 ,(6 ) ratios to theory reveals

that the PWBA-BC does not predict the inflection point

substantiated by the data, and the agreement between the

data and the PWBA-BC becomes worse as the atomic number of

the incident ion increases. Comparison of the PWBA modified

to include binding energy effects CPWBA-B) and the PWBA

modified to include Coulomb deflection effects (PWBA-C)

to the La, 2, Ly1 , and the Ly2 3 cross sections for protons,

alpha particles, and lithium ions incident on 70Yb indicates

that the PWBA-C overestimates the magnitude of the data but

does describe the shape of the L1-associated cross section

while the PWBA-B underestimates the magnitude of the data

but fails to predict the proper shape of the L1-associated

data. In order to evaluate the ability of the PWBA and the

presently accepted modifications to the PWBA to fit the

experimental data, future experimentation should be con-

ducted in the energy range that includes the point where

the ratio of the incident ion velocity to the L-Shell

electron velocity is equal to 0.19 (i.e., Vl/VL = 0.19).

This is where the L1-associated cross sections begin to

exhibit the shouldered structure and the cross section

ratios L3/L and L2/L have inflection points.

TABLE OF CONTENTS

LIST OF TABLES........0.......

LIST OF ILLUSTRATIONS .. 0 0..

Chapter

I. INTRODUCTION .. 0 0..

II. THEORY .. . . .

Page. . iv

. V

. . . .. 1

0 . . 9. 0. 0. . . . .. 7

BEAPWBAPWBA with ModificationsElectron Capture EffectsPolarization EffectsMolecular Orbital EffectsRelativistic Effects

III. EXPERIMENTAL TECHNIQUES AND DATA ANALYSIS . 28

IV. RESULTS AND DISCUSSION.......... ........... 39

V. CONCLUSIONS..............0......... ......60

REFERENCES.......................... ...........65

APPENDIX.......-................. . ...... .... 102

iii

LIST OF TABLES

Table Page

I. L-Shell X-Ray Production Cross Sections for1 471H, 2He and J i ons on Ce Nd M1 2e, 3Li 58 ' 60 625m,

66Dy, 67Ho, 7 0 Yb, and 82Pb. ......... . 71

II. L-Shell Cross Section Ratios. . ... ..... 86

III. Radiative and Nonradiative Rates Used toCalculate the Theoretical Cross Sections inThis Work ..*....*............. .. ......... 101

iv

LIST OF ILLUSTRATIONS

Figure Page

1. Conceptual Diagram of the Ionizing Process Dueto the Coulombic Interaction between theIncident Ion and the Target Electron . . . . . . 8

2. K-Shell Ionization Probability as a Functionof Impact Parameter for Protons on Selenium . . 10

3. The Experimental Arrangement at the RegionalNuclear Physics Laboratory Located at NorthTexas State University . . . . . . . . . . . . . 30

4. The Experimental Arrangement at the Oak RidgeNational Laboratory . . . . . . . . . . . . . . 33

5. The Experimental Arrangement at the FloridaState University Tandem Van de Graaff Laboratory 34

6. The L-Shell X-ray Transitions . . . . . . . . . 40

7. The La,2 X-ray Production Cross Sections for

Protons, Alpha Particles, and Lithium IonsIncident on 62Sm, 70Yb, and 82Pb . . . . . . . . 43

8. The Ly1 X-ray Production Cross Sections for

Protons, Alpha Particles, and Lithium IonsIncident on 62Sm, 70Yb, and 82Pb . . . . . . . . 45

9. The LY2,3,( 6 ) X-ray Production Cross Sections

for Protons, Alpha Particles, and Lithium IonsIncident on 62Sm, 70Yb, and 82Pb . . . . . . . . 46

10. The La 1 ,2 , Ly1 , and Ly2 ,3 X-ray Production

Cross Sections for Protons, Alpha Particles,and Lithium Ions Incident on 70Yb . . . . . . . 49

11. The La 1 2 /LY2 ,3 ,(6 ) Ratio for Protons, Alpha

Particles, and Lithium Ions Incident on 62Sm,

70Yb, and 82Pb . . . . . . . . . . . . . . . . . 51

V

12. The PWBA and PWBA-BC Theoretical La 12/LY2 3 (6 )Ratios for Protons, Alpha Particles, andLithium Ions Incident on 62Sm................52

13. The La,1 2/Ly2 ,3 Ratio for Lithium Ions Incident

on 58 Ce 60Nd, 66Dy, and 67Ho................53

14. The Ly1/Ly2 ,3 Ratio for Lithium Ions Incident

on 58Ce, 60Nd, 66Dy, and 67Ho.*..................54

15. The aL/aL Cross Section Ratio for Protons,

Alpha Particles, and Lithium Ions Incident on

6 2Sm and 82Pb . . . .0 . 0. . . . . 0. 0. . . . . 0. 0. 55

16. The Z1 Normalized Ratio of the La 1 , 2 X-ray

Production Cross Sections for Protons andAlpha Particles and Protons and LithiumIons Incident on 70Yb . . . . . . . . . . . . . . 57

17. The La 1,2 X-ray Production Cross Sections for

Lithium Ions Incident on 58Ce, 60Nd 62Sm,66Dy,

6 7Ho, 70Yb, and 82Pb a - * . . . . . 0. 0. 0. 0. *. 0. 59

18. The dependence of aLy on aL and aL and the

dependence of aLa on aL 'aL , and L for4 c1,2 L1 2 3

2He ions 70Yb........... .......... 105

19. The dependence of aL on aL and aL2 and the

dependence of aLa onaL'aLand aL for

4 1,2 1 2 3

2He ions on 82Pb.

vi

CHAPTER I

INTRODUCTION

In recent years extensive experimentation has been con-

ducted on inner-shell ionization processes and the related

x-ray production due to ion impact. These experiments have

provided information pertaining to the cross sections for

creating inner-shell vacancies and states of excitation due

to ion-atom collisions,1-3 thus providing an important

mechanism for analyzing the present-day theories from a

fundamental physics approach. The knowledge of the charac-

teristic ionization cross sections and the associated x-ray

production cross sections have already proved to be of

0 4practical importance in ion-implantation and trace analy.

sis.5,6

The creation of inner-shell atomic vacancies can be

accomplished by radioactive decay, 7 x-ray fluorescence, 8

or charged particle induced emission by electrons or

ions.10-32 Measurements of K- and L-Shell ionization pro-

cesses due to ion bombardment on various target systems

have been reported for protons, 10-17helium ions,13,15,18-23

24-26 27128 191 27-30lithium ions,4 carbon ions,7 nitrogen ions,9

and oxygen ions. 30-3 2 The reported data were in the form of

1

2

either the individual x-ray production cross sections for

resolvable transitions, such as the K , Ka., Ly, 2, LY2 ,3,(6)'

or the subshell ionization cross sections, such as K, L,

L2 , and L3'

Two basic categories of inner-shell excitation mechanism

for ion-atom collisions have been studied; first, the Coulomb

ionization10-27 where the interaction between the ion and

atomic electron is dominant, and, second, the electron pro-

motion mechanism3 3-3 5 where quasi-molecular orbitals are

formed during the collision. The parameters that determine

which excitation mechanism is dominant36 are the ratios

Z 1/Z2and v1 /ve where Z and Z2 are the atomic numbers of

the incident ion and target, respectively, v1 is the incident

ion velocity, and ve is the mean target electron velocity.

The direct Coulomb ionization is dominant for Z1 /Z2<<l or

v /v>>l. The electron promotion mechanism is dominant for

Z 1 /Z2~1 and vl/vel<<. In this work, direct Coulomb excitation

is considered to be the dominant mechanism since Z /Z_ is on

the order of 0.01 to 0.05 and 0. 0 9 vl/ve!O. 5 2 .

Theoretical models of inner-shell ionization by direct

Coulomb excitation have been developed from classical and

quantum mechanical approaches. The primary models that

have been used are the binary encounter approximation (BEA)

by Garcia, Gerjouy, and Welker,37 the constrained BEA (CBEA)

by Hansen,38 the semi-classical approximation (SCA) by Bang,

3

Hansteen, and Mosebekk,39,40 and the plane-wave Born approx-

imation (PWBA) by Choi, Merzbacher, and Khandelwal.41 All

four approaches have provided reasonable agreement with

experiment for K-shell ionization due to proton impact on

heavy elements.4 2'4 3 For the proton-induced L-shell processes

the BEA and CBEA have exhibited problems in predicting the

proper magnitude and energy dependence of the cross sec-

tions.10-12,15 The SCA has exhibited similar problems.44

However, the PWBA does provide the magnitude and energy

dependence for the L-Shell processes.

For 4 He and 7 Li ions1 3 '2 0 2 2' 24 '2 6 incident on heavy2 3

targets, the BEA and PWBA overpredict experimental x-ray

production cross sections at incident ion energies below

1 MeV/amu. The PWBA has been modified for the K-Shell and

46L-Shell by Basbas, Brandt and Laubert, and Brandt and

Lapicki, respectively, to incorporate the effects of

Coulomb deflection of the incident ion by the target nucleus

and increased binding energy of the target electrons due to

the penetration of the atomic shell by the ion. The former

modification has been designated as the PWBA with Coulomb

deflection modification or PWBA-C, and the latter has been

designated as the PWBA with binding energy modification or

PWBA-B. The incorporation of both modifications to the PWBA

has been represented as the PWBA-BC. These modifications,

which are more dominant at the lower incident ion velocities,

4

reduce the theoretical cross sections at the lower ion

energies and thus remove some of the discrepancies between

theory and experiment.13'21 '24'26

The PWBA has also been modified for the K-Shell by

Basbas et al.'4849 to include the effect of the polarization

ofthe initial state of the target electron by intermediate

and high velocity ions. This effect in essence adjusts the

electron orbit due to the presence of the incident ion in

such a way that the interaction between the ion and target

electron is no longer dependent on Z but a Z equal to

Z1 /(l-x) where x is proportioned to Z1/Z2'48 Wheeler et al.30

and McDaniel et al.28 have shown that the PWBA modified to

include Coulomb deflection, binding energy, and polarization

effects gives good agreement for K-Shell ionization data due

to carbon and nitrogen ion impact, respectively. The polar-

ization effect has not been considered in this work since

the maximum effect on the cross sections for the ions and

target materials studied would be on the order of 5%, since

Z 1 /Z2 s5%.

Recently the electron capture or charge transfer to the

projectile effect has been studied. Halpern et al.5 0 have

suggested that this effect is of the order of 1-2% for light

ions on heavy targets (targets of Z>10), and the work of Ford

et al.51 has shown this to be the case.

5

A detailed discussion of the excitation mechanisms

mentioned above is presented in Chapter II.

Since the ionization process basically consists of a

penetrating ion ejecting an orbital electron from a target

atom, the K- and L-Shell ionization processes are similar.

However, there are definite advantages to the investigation

of the L-Shell ionization processes since there are three sub-

shells and subsequently the L-Shell is more of the theory.

The advent of non-dispersive Si(Li) x-ray detectors52 and

subsequent improvements to the detection system have produced

resolution capabilities that allow the separation of the main

L-Shell x-ray components which are related to the L1, L2 , and

L3 subshell ionization cross sections (as discussed in Chapter

IV). This is not the case for the K-Shell since there is

only one level in the K-Shell.

The purpose of this work is to present a detailed

examination of the L-Shell ionization processes in the

region where the direct Coulomb ionization mechanism is

expected to be dominant. Presented is a study of protons

incident on 62Sm and 70Yb in the energy range of 0.3 to 2.4

MeV/amu, alpha particles incident on 62Sm, 70Yb, and 82Pb in

7the energy range 0.15 to 4.4 MeV/amu, and 3Li ions incident

on 58Ce60Nd 6 2Sm Dy, 67Ho 7 0Yb,and Pb at various

energies in the energy range of 0.9 to 4.8 MeV/amu. The

La 1 2/L, La 1 ,2/Ly, L'1 ,2 /LY2 ,3 ,(6 ), and the Lyl/LY2,3,( 6 )

6

intensity ratios have also been determined. The experimental

cross sections and intensity ratios have been compared to the

PWBA, the PWBA with Coulomb deflection modification (PWBA-C),

the PWBA with binding energy modification (PWBA-B), and the

PWBA with Coulomb deflection and binding energy modifications

(PWBA-BC).

CHAPTER II

THEORY

The purpose of this chapter is to present concepts and

a brief discussion of the various theoretical treatments

that have been formulated to describe the direct Coulomb

ionization of inner shell electrons due to ion impact.

Basic assumptions under which these theories apply are

discussed. The theoretical treatments will be discussed

under the headings BEA, PWBA, PWBA including Coulomb and/or

binding energy effects, electron capture, polarization

effects, and molecular orbital effects.

There are several requirements that are common to these

theories. Both the PWBA and BEA are valid for the cases

where Z1<<Z 2, i.e., light mass ions (Z1 ) are incident on

heavy target atoms (Z2), where Z1and Z2 are the atomic

numbers of the incident ion and target material, respectively.

Also, both approaches consider the primary interaction in

the ionizing process to be the Coulombic interaction between

the incident ion and the target electron as illustrated in

Figure 1.

Conceptually, the ionization cross section a can be

thought of as the probability of creating a vacancy in the

7

III

. 0

;-4 - "

O4- U0

r--4

IIIIII

4-J0 r~-4 U

0

r..C)

>I

8

I

NI C)C)~r4

HZ

C)

'H

C)

u C)

,doom,-dmr --- -- ---- - -- --.- -- ---

M

9

shell of interest at an impact parameter b integrated over

all the impact parameters. This can be represented as

a, = f 2'r P(b)bdb, (11-1)0

where P(b) is the probability that an ion (impingent on

the target atom along the x-axis from negative infinity at

an impact parameter b) will remove the target electron from

its initial state. The impact parameter b is approximately

equal to (Z1 Z2e2/2E) [tan(6O) ]~ , where E is the incident ion

energy and 0 is the incident ion scattering angle measured

in the C. M. frame (14). One would expect that as the impact

parameter b goes from zero to infinity, the probability of

the ionization of a given shell would decrease and approach

zero as b becomes greater than the shell radius. This

effect is shown in the investigations by Cocke5 3 and

Laegsgaard et al. 54 of the K-Shell ionization dependence on

the impact parameter b. Figure 2 shows P(b) as a function

of b for protons in 34 Se, where K-Shell radius is approxi-

mately 0.015. Stiebing et al.1 4 have studied the L-Shell

impact parameter dependence for Pb and their data exhibit

the same trend.

Requiring Z2<<Z is equivalent to requiring r1/r 2 l,

where rI is the K-Shell radius of the projectile and r2 is

10

2MeV Proton Ionization of SeleniumK-Shell

6 (Ref. 54)

4

o

-r-0

0

0.00.01 rK 0.02Impact Parameter h(5i)

Figure 2

11

the shell radius of interest of the target atom. For low

velocity heavy ion inner-shell excitation, i.e., where Z1 /Z2-l

and thus r1 /r2~1, strong disagreements between direct Coulomb

ionization theories and the experimental data have been ob-

served. 33,55,56Hopkins5 studied chlorine ions incident on

carbon and Matthews et al.56 studied fluorine ions incident

on neon, argon, and krypton, and both report charge transfer

or electron capture effects. Meyerhof et al.33 have studied

symmetric and near symmetric ion-target systems (i.e.,

Z 1 Z2 ) in order to observe the molecular orbital formulation

during the collision.

BEA

The BEA is a classical description of the ionization

process based on acollision of the incident ion having a

velocity v and a target electron with a velocity v2 . Garcia

et al. 3 7 developed a scaling law that made use of the ls

non-relativistic hydrogenic wavefunctions as a basis for

the velocity distribution of the target electrons. A

detailed discussion and comparison to data are presented by

.42 43Garcia et al. Lear et al., for example, illustrate the

success the BEA has had for predicting K-Shell vacancy

production for H ions on various targets from Fe to As.

Hansen,38 McGuire and Richard,57 and McGuire and

Omidvar58 have tabulated values for the BEA from which L-Shell

cross sections can be computed. McGuire and Richard5 7 made

12

use of is non-relativistic hydrogenic momentum wavefunctions

and McGuire and Omidvar5 8 used 2s and 2p nonrelativistic

hydrogenic momentum wavefunctions as a basis for the target

electron velocity distribution.

The BEA ionization cross section is given by 58

o(v) = f p(v 2) 2 dv 1El eff d(AE), (11-2)0 2 v2 2 d(AB)

= NZ2a0 G(V), (11-3)

U2

where N is the number of electrons in the filled shell,

V = v1 /V0 = (melectron E1/M1U) and is referred to as the

scaled velocity, U is the binding energy of the electron

shell, Z is the projectile atomic number, a0=6.56x104 (KeV)2

-barns, and G(V) results from the integration of Eq. 11-2

w d eff . . 59-60with d(AE) given in closed form by Garcia. The electron

velocity distribution p(v2 ) is equal to 0*(v 2)(v 2) where

D(v 2)is the momentum space wavefunction for the target

electron. E1 and M1 are the ion energy and mass, respectively.

The works of Abrath and Gray1 1 for 1H ions incident on1

6 2 Sm and various other rare earths, Shafroth et al.62or

protons on gold, and Madison et al.12 for H ions on lead1

and bismuth have shown that the BEA has difficulty predicting

the magnitude and shape of the L-subshell vacancy production

cross sections, particularly the magnitude and shape associated

13

with the L subshell. The structure of the L subshell

vacancy production cross section as a function of incident

ion energy results from the 2s nature of the L subshell

electrons and has been well documented (see, for example,

ref. 11, 12, 16, 17 and 24). It has been pointed out by

McGuire63 that the failure of the BEA to adequately describe

the 2s ionization process may require an indepth restructuring

of the fundamental approach used within the framework of the

BEA theory.

The approach of Hansen,38 referred to as the constrained

BEA or CBEA, is similar to that of McGuire and Omidvar58 with

the exception that the CBEA calculations are performed in

configuration space instead of momentum space. The works

of various authors (see, for example,ref. 10, 11, 15, and 17)

have demonstrated that the CBEA also has problems in pre-

dicting magnitude and shape of the L subshell vacancy

production cross sections.

PWBA

A quantum mechanical description of inner-shell ioni-

zation by fast ions was originally derived in 1930 by Bethe64

who made use of the Born approximation; i.e., the exact

eigenfunction was replaced by the product of a plane wave

and an unperturbed atomic state. The PWBA is based on the

assumption that the interaction between the incident ion

and the target electron is weak, which means that the

14

scattered wave is small. This allows the use of first order

perturbation theory.

The PWBA is considered to be valid if the following

criteria are satisfied. First, the incident ion is in the

high velocity range, where (Zie2/Xiv)<<1, and thus the initial

and final particle states can be treated as plane waves.

Second, the projectile acts as a point charge. Third, the

states of the target electrons are those of the unperturbed

target. And finally, the atomic number of the incident ion

Z is much less than the atomic number of the target Z2 '

Under these conditions, the cross section is pro-

portional to the square of the transition matrix given by

Vfr K2)~f~ K (~)~r ), (11-4)V = <@Kf If K.11i 214

where $i(r2) refers to the initial atomic state of the target

electron, Pf(r 2) is the final state of the electron,

K ++Kf-rl

K. (rl) = eiirl and K (r ) = eK(i.e., the initial

and final particle states treated as plane waves), and

Irl-r2| is the separation between the ion and the atomic

electron.

The differential cross section is given by the expres-

.65sion

22 2dc =16TrZ 2 e 2 dq F (q) de, (11-5)

1 q

15

where 6 is the energy transfer in the collision and q is the

momentum transfer, i.e., q = IKf-KiI. Choi, Merzbacher, and

Khandelwal4 1 used 2s and 2p non-relativistic hydrogenic wave-

functions parameterized in terms of an effective charge,6 6

Z 2s= (Z2-4.15), to evaluate the form factor

IF (q)I = <$f(r 2) jei92 ir 2)>. (11-6)

The cross sections for the K- and L-Shells are calculated in

terms of quantities W=-AE and Q q2 2 ', where n is the

nE2 s Z2s

principle quantum number, q is the momentum transfer, ao is

Z2the Bohr radius for hydrogen, and E2s= 2s (13.6 eV). In

n2

these terms the differential cross section is

22 2 2d2aL 87TZ2 e dQ F 2 a 2WL 1 hv1 2 W,L (Q)dW.(-7)

2s

2 v2 v2

21 0 dQW4 Q 2S Z4 v2 FWL.(Q) . (II-8)

2s 1

2 2a q~

Integration of Eq. 11-8 from Q . = min-to Q =moxandmmn 7 max

2s

Wmin = U 25/n2 E2 s to Wmax = yields the L-subshell ionization

cross section. For convenience, the notation has been

shortened to

16

2a2

UL = 8vZa L. L., L.L. 8Tr 1 4 fL -n ! L(1 -9

1 Z2srL.1

m Ewhere L= e e1 with m = electron mass, M = ion mass,

1 M Z e11 2s c

Ro, = 13.6eV is Rydberg's constant, and

f L.T1L,0 L f001L. TLW)dW. (II-10)

1 L. 1 1

4

In the above expression, IL. is the excitation function for

the L subshell6 7 and 0 L =14 I . The values of fL. "L,6L.

Z2 R2soO

are tabulated by Choi et al. 41

PWBA with Modifications

Discrepancies between PWBA and experimental data have

been observed (see, for example, ref. 10, 15, 16, 17, 20, 24)

for low projectile velocities. Brandt and Lapicki4 7 have

suggested modifications to the PWBA for the L-Shell that

treat the perturbation of the electron states due to the

close proximity of the projectile at the time of ionization

as well as the perturbation of the incident ion trajectory

caused by the ion-nucleus Coulombic interaction.

17

The first effect is referred to as the binding energy

effect (PWBA-B). Since the ion has to penetrate the L-Shell

to cause ionization at low ion velocities, the electrons

become more tightly bound to the L-Shell region. At the

lower particle velocities, the atomic electrons have time

to adjust to the presence of the ion and become more tightly

bound to the region of the shell, thus the likelihood of ion-

ization is reduced. This perturbation is considered to be

small and can thus be treated as an addition to the electron

binding energy6 8 as

z 2L.UL. =UL. + <4 L. (12) +l + Lr 2)>

1 r 1 -r2

where $L. are screened hydrogenic wavefunctions, and r1 is1

evaluated at the closest internuclear distance R. Using

the straight line trajectory, R0 equals the impact parameter

b. With y=_ Z2sb/aO, the effective binding energy factor

. 46can be given as

8Z 1-e(1+ 3 +/4y 2 +172 CL.3

2s()= 1 + Z 2s6 y (II1-12)2s Z2s 0L. y

1

and CL is a constant with the values of 9, 7, and 4 for the L,

L2 , and L3 subshells, respectively. The binding energy factor

18

e is averaged over all impact parameters weighted by the

Bang-Hansteen-Mosebekk ionization probability39,40 so that

2Z6L L = 1 + g z (11-13)

1 1 Lj2s 1 1

2v1where 2 = v and the values of g are given in

i L L1 1

analytic form.4 The PWBA with binding energy modifications

(PWBA-B) are calculated from the expression

Z 22 1aL.-= 87ra0 fLEL) . (11-14)

1 Z2 sL. 1 1 1

Lapicki and Losonsky69 have recently made a correction

to Eq. 11-12 in the calculation of the binding energy such

that CL. now takes the values of 9 and 3 for the L1and

L2 ,3 subshells, respectively. However, this correction is

small and thus has not been included in the PWBA-B theory

used in this research.

The second effect is referred to as the PWBA modified

for Coulomb deflection (PWBA-C). This modification allows

for the deflection of the incident ion from its straight

line path due to the Coulomb repulsion expected by the target

nucleus on the ion. This effect was first studied using a

classical approach by Bang, Hansteen and Mosebekk.3 9 ,4 0

This effect has been incorporated into the PWBA by the

expression

19

GPWBA-(-=(n -1) Es (rdq)PWBA, (11-15)

where n = 10 for L and n = 12 for L2 and L3'

d=eZ1Z12(m -+M1 )/v2 with Z ,'M ,%Z2, and M2 referring to

the incident ion (subscript 1) atomic number and mass and

the target atomic number and mass, respectively; and v1 is

the incident ion velocity, and qs is the minimum momentum

transfer in the direct ionization to the continuum state of

the target atom. In Eq. 11-15, E n(Trdq) is the exponentials

integral of order n, i.e.,

E (x) = ft-se-xtdt, (11-16)ns

and can be approximated by

(n5 -1) -E (x)~ nS1 e (II-17)

S (n--1+x)S

as suggested by Brandt and Lapicki.47

A combination of both modifications to the PWBA (PWBA-BC)

is calculated by the expression

Z2 (n -1) e - dEqsa 8'rA 21 Sf IE:e(11-18)

s 1 1

Electron Capture Effects

Electron capture effects can occur in two ways. First,

a target electron in an inner-shell is captured into a bound

state of the incident ion; and second, a target electron in

an inner-shell can be captured into a continuum state of the

incident ion. Both of these effects increase as the ratio

Z l/Z2 increases.

The first effect often referred to as innershell pickup5 0

70 71was derived by Oppenheimer -Brinkman-Kramers (OBK approxi-

mation). Omidvar72 has given the cross section for electron

capture to a bound state by a particle of velocity v1 as

7an2 e 8 4 OBK - Ta0n2 28e Z1 5 62 -5Oss' 03 22 (1-) [l+-5] , (11-19)

5n3f v T 2 a

where n1 and n2 are the principal quantum numbers of the elec-

trons in the s and s' shells, respectively, a = Z2 /n2a0 , and

2 2 2 2e2 hv Z z

2

= e [V-1 ( 2 1

2a0 v1 e n2 n

Using screened hydrogenic wavefunctions and a binding energy

2 731/2 v2 ses, Nikolaev derived Eq. 11-19 but with orbital

velocities described in terms of an effective Z (i.e.,

Z2K = Z2-0.3 and Z =2L Z2-4.15). This cross section is

denoted as aB(0 ).

20

21

Lapicki and Losonsky69 have modified the OBK calcu-

lations for low velocity ions to include Coulomb deflection

and binding energy effects. The binding energy effect is

iOBKincorporated into ss, by an increase in binding energy

represented by Eq. II-11. The binding energy reduces the

electron capture by increasing the electron binding energy

from Os to e6s. This effect has been incorporated into

rOBK hat aOBbK 69ss, becomes

B =OBK(F0(11-20)

ss ' oss ' s

The Coulomb deflection modification is incorporated

into the OBK theory by comparing the Coulomb and plane

waves at the origin.74 As with the PWBA, the Coulomb

deflection is incorporated into the OBK theory. The electron

capture cross section becomes

ass,= exp[-adss'qss,(0s)](OBK s),0(II-21)sss s ~ss , 1121

where dss' d 1/2PM1 -= -+M~21/2 1 2'

1 2v2 _12v2 )1-E 1 M

v1

22

Coulomb deflection and binding energy effect have been

incorporated into the theory for electron capture from s

to s' shell for low velocity ions as

a '(v<<V expff ds, qs, ('e aOBK (Ess ( 1 2s' 1 s,) =xs)ss'sS

(11-22)

McDaniel et al.75 have recently shown that

a ss, (v1 V2s'v 1 s,) gives agreement to within a factor of

2 to 4 for28Si+q ions on Sc TiCu,and 32Ge.1421 c, 22Ti, 29 Cu an 2G

Electron capture to the bound state has been neglected

in this work since for all ion-target combinations

z 5z1 /Z2 <<,and electron capture is proportional to (Z1 /Z2 )

The second electron capture process is electron capture

to the continuum of the ion. Lapicki and Losonsky69 have

estimated the electron capture cross section to the con-

tinuum (a OBK) to besc

a v (2-v 2 2 +4 2 5

OBK =sk [1+(v2s vk)/vl] 2 + 42-ksc Z 3 2 2 )k , (I-23)

2Z1 (v1 +v2 s 1

where ask is the cross section for electron capture to the

K-Shell. In the limits of low and high velocities or when

v2sv lk (i'e., Z 2/n 2 >>Z1 /n) the expression in the brackets

is approximately equal to one. Therefore, electron capture

to the continuum is at least 2Z3 times less than the electron1

23

capture cross section to the K-Shell. For the ions and

velocity range of this paper, electron capture to the con-

tinuum state of the ion is negligible.

Polarization Effect

The polarization effect becomes important for heavy,

fast incident ions of charge Z 1 e. This effect has been

studied from a classical approach76 and a quantum mechanical

approach. Both approaches treat the bound atomic electron

as an isotropic harmonic oscillator having a frequency w.

Also, both approaches deal only with distant collision

which correspond to large impact parameters. This allows

the multipole expansion in powers of the projectile-target

distance.

The interaction potential between a classical particle

[with coordinates X(t), Y(t), and Z(t)] having a charge

Z1 e and an electron (with coordinates x,y,z) relative to

the atomic nucleus as the origin is

V(t)= = 1 (11-24)|R(t)-rf

= Ze2 1 + R(t)-r + 1 3[R(t)-r]2 r2

[R(t)]3 [R(t)1 5 [R(t)]

3+ O(!T) ] (11-25)

R

24

for R(t)>>r. The l/R, r/R2, and r2/R3 terms are referred to

as the monopole, dipole, and quadrapole terms, respectively.

The subsequent Hamiltonian used to describe the motion is the

sum of an unperturbed part which consists of the harmonic

oscillator Hamiltonian plus the dipole potential term and

a perturbed part which consists of the quadrapole potential

term. The monopole term is neglected since the initial and

final states are orthogonal. The particle is also assumed

to travel in a straight line trajectory.

At high velocities Hill and Merzbacher7 7 state that the3

Z polarization contribution to the cross section depends

logarithmically on the parameter a w/v1 , where a is a lower

limit of the impact parameter integration, w is the oscillator

frequency, and v is the incident ion velocity. Consequently,

when a w/v1<<1, the polarization terms depends weakly on the

choice of a. Furthermore, small impact parameters should

contribute little since close collisions with high velocity

ions are considered as pure Coulomb interactions with the

target electron, considered to be free, and result in con-

tributions of over ZI only. Basbas et al. have calculated

the polarization modification factor for the PWBA to describe

the K-Shell ionization process as

I PWBA l 2 3 3oo I(wa2 K) dwK =[1 + ( -) (q0 a2 K) f 2 ()KK vK(wO2KK 2K 1 f(-a26

(11-26)

25

where I(wa2K) has been evaluated,76 K(w) is defined as the

differential oscillator strength, and a PWBA is defined as

PWBA Z1)2 2 2a =(7) 8ra0 ( 2v0/ 1) f a0) (II-27)

Z2

Thus the polarization term is of the order (Z /Z2) 3, and can

be expected to be a small effect.

Molecular Orbital Effect

The molecular orbital (MO) effect becomes dominant only

in symmetric or near symmetric collision processes (i.e.,

Z1 -Z2 ). In this region, the MO effect completely dominates

the direct-Coulomb mechanism.

Conceptually, the MO mechanism can be viewed as the

short time formation of a molecule consisting of the incident

ion and target atom with the associated rearrangement of

electron orbitals. A detailed discussion of the MO effect

for Br, Kr, I, Xe, and Pb ions in symmetric and near sym-

metric collisions has been presented by Meyerhof et al.3 3

The MO effect has not been considered in this work since

the maximum value of the ratio Z1/Z2 = 0.05, and this effect

becomes important only in slow collisions involving ion-

target combinations where Z1 /Z 2 'l.

Relativistic Effect

Hansen3 8 has suggested that the relativistic effect can

be included in the calculations of the cross sections by

26

correcting the electron velocity and mass. The relativistic

velocity and mass would be given by

vrel = [R/(l+R)]1/2c (11-27)

and2

m = m0 l 2 1/20 2c

where R = (E/m0 c2) 2 + 2(Ee/m0 c2)

The magnitude of the relativistic correction increases

at low incident ion energies, and tends to increase the cross

sections for the middle and high Z target materials. Hansen

has tabulated the ratio of the cross section calculated with

and without relativistic corrections (i.e., arel/a nonrel)

2for several (v1 /v) values for Z = 29, 47, 73, and 92, where

v is the average shell electron velocity. For the elements

and velocity range of this study, the relativistic cross

sections would be greater by 4-10% than the non-relativistic

cross sections at the low velocities with the discrepancy

decreasing to about 1% at the higher velocities.

Choi78 has calculated the L-Shell ionization cross

sections using relativistic wavefunctions. The cross sections

are calculated in the same manner as the non-relativistic PWBA

with the difference being that the relativistic excitation

function IL.(nL'WL) is explicitly dependent on ZL while the1 1

27

non-relativistic excitation function does not explicitly

depend on ZL.

The relativistic correction has exhibited problems in

predicting data. The work of Chen1 7 for1H ions on7Pt,1748

79Au, and 80Hg and the work of Datz et al. 74 for 1H ions

471and 2He ions on 79Au as well as the work of others13 have

shown that the relativistic PWBA overestimates the data by

at least 20% over an energy range similar to the range of this

work. Choi78 has suggested that this discrepancy could be

due to the fact that his theory has not included Coulomb

deflection effects. Relativistic effects have not been

included in this work.

CHAPTER III

EXPERIMENTAL TECHNIQUES AND DATA ANALYSIS

For all incident ion-target combinations over the

energy ranges studied, the forward nuclear scattering was

Rutherford in nature. The absolute magnitudes of the ex-

perimental x-ray production cross sections were obtained

by normalizing the x-ray yields to the Rutherford differen-

tial cross sections of the incident ions. The incident ion

beams (ranging from the order of 1 microampere for H and

4He ions to the order of 10 nanoamperes for Li ions) were2 3

collimated before entering the target chamber. Thin targets

were mounted at a 450 angle relative to the incident ion

direction. The targets were prepared on 10-50 microgram/cm2

carbon backings using standard evaporation techniques. The

target thicknesses were determined by measuring the nuclear

1elastic scattering of H ions of energy 1-2 MeV from the

respective targets. The thickness can be calculated from the

following expression:

PAx = C ( -1)I (da/dQ)dQNp 0

where C is the number of back scattered particles detected

28

29

by the particle detector, Ip is the integrated charge at the

target divided by the unit proton charge, (da/dQ) is the

Rutherford differential cross section, dQ is the solid angle

subtended by the particle detector, A is the atomic number

of the target atom, and N0 is Avogadros number. The thick-

ness (pAx) has the units of grams/cm2. The target thick-

2nesses were 10-65 micrograms/cm2. The recent investigation

by Schiebel et al. on the effects of target thickness and

incident ion atomic number on the L-Shell ionization pro-

cesses showed that no correction for such effects was

required for 1H,2He, and 3Li ions incident on rare earth

and 82Pb targets of these thicknesses.

The x-ray yield data was stored on magnetic tape during

the experiment. Later, the data was spectrally analyzed

using the computer code SAMPO8 0 which performed peak

location, peak fitting, and peak stripping.

The low energy work involving 1 H ions of energy less

than 2.5 MeV and 4 He ions of energy less than 0.6 MeV/amu2

was conducted at the Regional Nuclear Physics Laboratory

located at North Texas State University utilizing the 2.5

MV Van de Graaff accelerator.

The experimental arrangement for the facility is shown

in Figure 3. Four silicon surface-barrier particle detectors

were positioned at angles of 300, 450, 135*, and 1500

relative to the incident beam direction to detect the

30

-4J

0

014 j-0u .4-JUO

C) uo

U4

Ou

o1-4 u

4-J O-H

0

4--Jv4

4-)

CT

C3;io

31

protons and alpha particles elastically scattered from the

target material. The solid angles of the particle detectors

were measured using a calibrated 244Cm source positioned in

the target location.

A Kevex-ray Si.(Li) x-ray detector with a full width

half maximum (FWHM) resolution of 190 eV at 5.898 KeV was

positioned directly outside the target chamber at a 900

angle relative to the incident ion beam direction and about

8 cm from the target. A 0.0254-cm mylar window separated

the high vacuum target environment from the Si(Li) detector

environment. The x-rays detected had to travel through the

0.0254-cm mylar window, approximately 8 cm of air, and a

0.00254-cm Be detector window.

The study of the 42He and 7Li ions incident on6Sm,

70 Yb,and 8 2Pb targets in the energy range above 3 MeV was

performed using the model EN tandem Van de Graaff acceler-

ator at the High Voltage Laboratory, Oak Ridge National

Laboratory (ORNL). Ion beams of 2Heand Li were obtained2 3

in charge states of 2+ and 3+, respectively. An ORTEC Si(Li)

x-ray detector with a FWHM resolution of 175 eV at 5.898 KeV

was positioned inside the target environment at a 900 angle

relative to the incident ion beam direction and approximately

5 cm from the target.

Silicon surface-barrier detectors were positioned at

300 and 45* relative to the incident beam axis to measure

32

the elastically scattered He and7Li ions. The measured2 3solid angles for the 300 and 450 particle detectors were

3.05 x 10-3 and 8.16 x 10~4sr, respectively. The experi-

mental arrangement is shown in Figure 4.

The study of the 7Li ions incident on CeNdDy,3 58 60Nd, 66 Dyand 67Ho in the energy range of 2.0 to 4.8 MeV/amu was

conducted at the Florida State University Tandem Van de

Graaff accelerator Laboratory. The Si(Li) x-ray detector

with a FWHM resolution of 190 eV at 5.898 KeV was positioned

outside the target environment. The target chamber was

constructed with the silicon surface-barrier detector

mounted on a swivelling radial arm with the axis of rotation

about the target position. This allowed the particle detector

to be positioned at any angle between 50 and 175' relative

to the beam axis. See Figure 5. In order to replace

targets, the particle detector had to be moved thus causing

the geometry to change for each set of targets. During the

L-Shell experiment, the 37Rb K-Shell target was mounted

on the same rod as the 58Ce, 60Nd, 66Dy, and 67Ho L-Shell

targets. Due to the non-Rutherford scattering observed

7for the 3Li ions on Rb above 21 MeV, the integrated3 37charge (collected in a Faraday cup downstream of the tar-

gets) as well as the nuclear scattered particles were

measured. The 37Rb x-ray production cross sections were

obtained by normalizing the x-ray yields to the integrated

LAl

I Jw/w// '

- TI

aseI!

A

1111 1 -X-xJbhbaka hv

L

I I UJ

I

33

I

Ij "r

Ir 9m

-

-

bi

>1

o.

4

(a

e44)

r-4 4J.00

0oa)

+ 4J)

0 0>

0 PE) 4

irnrtn

34

041U

41)

4f

C)

ra .r.EQ)

LO

-0

35

charge. The 37Rb K-Shell results were reported by McDaniel

26 7et al. From the 37Rb data for 3Iti ions below 21 MeV,

the ratio

d2

4 - (III-2)sin4 (0/2)

was extracted. Here dQ is the solid angle subtended by the

particle detector and 0 is the angle relative to the beam

axis at which the particle detector is located.

The absolute efficiencies of the Si(Li) detector sys-

tems used were measured using standard calibrated souces

of 51Cr, 54M 55n, Fe,57Co, 65Zn, and 241Am. The procedures

used to measure the efficiencies have been outlined by

Magnusson,81 Hansen et al.,82 and Gehrke and Lokken.83 The

efficiency was found by utilizing the following expression:

Nx

I t (111-3)x

where e is the efficiency of the detector at the x-ray

energy, N is the integrated number of counts in the source

peak, Ix is the calibrated source strength in curies at the

time of the measurement, and t is the time the detector was

in the counting mode. The sources were positioned at the

target location in the target chamber under vacuum in order

to simulate the experimental situation. Thus, the absolute

efficiency was dependent upon the intrinsic efficiency, the

36

solid angle intercepted by the detector, and x-ray atten-

uation of the mylar, air, and Be.

The individual L-Shell component x-ray production cross

sections were obtained in the following manner:

K(YLa -B)

1,2 La

K(YLy -B)

ay - (III-5)by1 Ly1

K(YL -B)

abY ()2, 3,(6) , (111-6)Y2 ,3,(6)

where YLal,2-B, YLy -B, andYLY2,3,(6) -B are the respective

experimentally measured x-ray yields with background sub-

tracted, CLa 1 ,2 Ly,. and ELy2 3 ,(6 ) are the Si(Li) detector

efficiencies for the respective x-ray lines, and

1.2965 x 10(-3Z 1z2 ) 2 tR dQK = 2 4 '(111-7)

YR E t sin (0/2)

In Eq. (111-7), Z1 and Z2 are the atomic numbers of the

incident ion and target, respectively, YR is the experi-

mentally measured Rutherford yield, E is the incident ion

energy in MeV, and tR and tx are the respective dead time

37

corrections for the particle detector and x-ray detector

(i.e., tR is equal to the true time for counting multiplied

by the factor one minus the fraction of time the particle

detector was not counting). The dead times were kept below

10% for both detectors throughout the experiments.

The x-ray production cross section data are presented

in Table I, and the La,1 2 /Ly1 , La 1,2 /LY2 ,3 ,(6 ) and the

Lyl/LY2 ,3 ,(6 ) ratios are listed in Table II.

The error analysis for the data taken at the NTSU

Regional Laboratory and ORNL includes two main categories:

(1) the relative uncertainty which consists of statistical

errors associated with the individual x-ray and charged

particle elastic scattering yields (2-10% and 1-8%, respec-

tively) and (2) the overall normalization uncertainty which

contains contributions from calibrated source strength error

(3%), x-ray source branching ratio uncertainties (1-2%),

charged particle detector solid angle error (3%) and the

uncertainty in Rutherford scattering cross section through

the detector angle (<5%).

The data taken at Florida State University consists

of the same errors as above, except that the error due to

the uncertainty in the charged particle detector solid angle

is inseparable from the uncertainty in the particle detector

angle. The uncertainty in the ratio do is 10%.s4-i----sin (0/2)

38

For all the data, the relative uncertainties for the

L, La1 ,2, Ly, and Ly2,3,(6) x-ray transitions were <6%,

<3%, <11%, and <11%, respectively. For the NTSU and ORNL

data, the total uncertainties were 10% for Lt, <9% for

LalP2,and <14% for the Ly1 and Ly2 ,3 lines.

For the FSU data the total uncertainties were 11% for

L9, 10% for La,1 2' and 15% for the Ly1 and Ly2 ,3 lines.

All theoretical calculations used in this work were

obtained using the computed code XCODE developed by Pepper. 84

CHAPTER IV

RESULTS AND DISCUSSION

The predominant x-ray transitions due to L-Shell

ionization are schematically depicted in Figure 6. This

shows that a'. has a 2s (9,=O) nature and aL and aL3 haveL 1 L 2 L3a 2p (9=l) nature. The x-ray production cross sections for

the Lk, La 1,2 , Lyl, and LY 2 ,3,(6) transitions are related

to the vacancy production cross sections by the following

expressions -(where L, L2, and L3 correspond to LI, LII,

and LIII):

Lk L + f23 aL + (f12 23 f13'L > 33 2 1 (I-l

Lt 1 ,2 [L3+ f2 3aL2+ (f12f23+f13L)ab 1 3 13a '3r3

(IV-2)r

Ly a L2+fl2 aL] r2y , (IV-3)

aL a L W 1 r 'Y +r2 'Y3 + [aL +f12aL ]W2r2y623,(6) 1 r1 2 1 r1 1

(IV-4)

where the aL 's are the respective vacancy production

39

Iv

II. -~-I1 I -

VII

VIIV

III L

II1i

y 3

l- _

LTai____

V- Lal

4 IIIL

II ~

L X-RAY TRANS ITIONS

Figure 6

40

0

TI t

55555

22I10

a5/23/23/21/21/2

7/25/25/23/23/21/21/2

5/23/23/21/2

1/2

3/21/21/2

4 34 34 242S11411~40

3 23 2

3 13 13 0

222

1I0

LBa

Id

41

cross sections, the w's, f. .'s, r,'s, and r 's are the

fluorescence yields, the Coster-Kronig transition coeffi-

cients, and the partial and total radiative widths,

respectively. The fluorescence yield w is the average

number of de-excitations of the L. subshell that emit x-rays

divided by the number of vacancies in the ith subshell. TheCoster-Kronig transition coefficient is the probability

that a vacancy produced in the ith subshell will be filled

by an electron in the jth subshell thus leaving a vacancy

in the j subshell. This can be viewed as a vacancy

migration from the ith subshell to the jth subshell. Thepartial radiative width r. is the probability that an "x"

x-ray will be emitted when the Li subshell is ionized and

the total radiative width ri is the sum of all the partial

radiative widths for the ith subshell. The values of the

fluorescence yields and the Coster-Kronig coefficients

used in this work were taken from Bambynek et al.85 and

the radiative widths were taken from Scofield.86 These

values are listed in Table 3.

For the targets and the energy range studied here, it can

be shown that the Lk and the La 1 ,2 x-ray production cross

sections are dominated by the L3 ionization cross section,the LyI x-ray production cross section is dominated by the

L2 ionization cross section, and the LY 2 ,3,(6) is dominated

by the LI ionization cross section for target Z-76, where

42

S2y 6is very small. For higher atomic number targets, r2yis no longer negligible, and thus Ly 2 ,3 ,(6 ) begins to lose

its total L1 characteristic. (See Appendix.)

In this work, the x-ray production cross sections are

measured and reported. When vacancy production cross

sections are reported here, they have been derived by

using the experimentally measured x-ray production cross

sections in Eq. IV-1 to Eq. IV-4.

The La 1 ,2 , Ly, and LY2 ,3,(6 ) x-ray production cross

sections for1H,4 He, and Li ions on Yb and 8 2Pb and for4 72He and 3Li ions on 6 2Sm are shown in Figures 7, 8, and 9,respectively. The experimental data are compared to the

PWBA and PWBA-BC. The La 1 ,2 x-rays are from the M-Shell

(M4 ,5) to the L-Shell (L3), the Ly1 x-rays are from the

N-Shell (N4) to the L-Shell (L2), and the Ly2 ,3 x-rays are

from the N-Shell (N2 ,3) to the L-Shell (L1).

From Figure 7, it is apparent that the PWBA-BC is in

better agreement with the La 1 2 data than the PWBA for each

ion specie incident on all three target materials. However,

in the case of the 82Pb cross sections, the PWBA-BC pre-

dictions begin to underestimate the observed La 1 2 for

incident ion energies less than 1.2 MeV/amu. The discrep-

ancy increases as the incident ion energy decreases and as

the ion atomic number increases. The maximum discrepancy

is on the order of 20% and could be due to the fact that

10

10

10

id

(r~x 10,( b)

10(

11cr

101

106

Figure 7

43

- ,T,

1H-- PWBA

- PWBA-BC

-

a---** -0Yb

42He

2 P.04

3Li

S62S

- 70 Yb

A82 Pb

S 1.0 2.0 &.0 4.0 &.0

E /M (MeV/amu)

44

relativistic effects have not been included in the PWBA-BC.

This discrepancy between theory and data has. also been ob-

served by Chen1 7 for protons on Pt, Au, and Hg and by Brandt

47and Lapicki in their analysis of the Au data taken by Datz

et al. 22

The Ly1 x-ray production cross sections are shown in

Figure 8 and indicate that the PWBA is in better agreement with

the data than the PWBA-BC with some deviation observed at the

lower ion velocities for Li ions. These results are also in

agreement with the findings of Brandt and Lapicki47 and Chen.1 7

Figure 9 shows the LY2,3,( 6) x-ray production cross

sections. This figure demonstrates the same general trends

as observed for the Ly, data. The PWBA gives an overall

better representation of the data than the PWBA-BC. However,

it is important to note that neither theory properly predicts

the shouldered structure of the LY2,3,( 6 ) data. This has also

been observed by Chen.1 7

It is apparent that the PWBA-BC does not adequately

describe the Ly1 and Ly2,3,( 6 ) x-ray production cross

sections for incident ions which have energies less than

0.8 MeV/amu. Brandt and Lapicki47 suggest that the uncer-

tainties in the radiative and nonradiative parameters are

of the same order of magnitude as the discrepancies between

the data and the PWBA-BC, and thus could be responsible for

the disagreement. This suggestion may have some validity

I0I

100

1-110

10

10F

2,10

100

lo~

I0F

Kr,

1PWBA

PWBA-BC

-I I

Plli

* - * * - - - 0 01

-000 , - **-

- 62

- * 77

82',

_L 1 1 i I I I I I i t ii i 1i i i 1 4 1 1 1 .1

0 1.0 2.0 3.0 4.0 5.0E/M (MeV/amu)

Figure 8

45

Sm

Pb

0 0

-0 H

---PWBA

-- PWBA-BC

0 LX 100(b)

10

I0

-II0

10~0

- *H

- /

* 62-

0*

A l

o 70Yb

amp 00,/

I82Pb

1 11 -. I I I . .t, L

1.0 2.0 3.0 4.0

E/M (MeV/amu)

Figure 9

46

101

0o

C2

~1~

5.0

-

wmwv

i i 1 .1 1

47

since the fluorescence yields are experimentally known to

about 10%,85 the Coster-Kronig coefficients are experimentally

quoted to about 25% or less,85 and the radiative widths are

theoretically calculated to about 3% or less.86 These errors

do seem to be somewhat larger for the L subshell related

processes (LY2,3,(6)), but those related to the L2 processes

(Lyl) are usually of the same order as those related to the

L3 (La 1 ,2 ) processes. Thus, the L2 and L3 processes should

show similar trends in comparison to the theories, but they

do not. Thus, there appear to be some problems associated

with the binding energy modification which are independent of

these radiative and nonradiative parameters if it is assumed

that these parameters do not change significantly as a function

1 4 7of ion energy for 1H 2He, and 7Li ions on elements having

atomic numbers in the range of the elements considered here.

Evidence does exist for such an assumption. For example, high

resolution work of Pepper et al.31 for 160 ions incident on8

several rare earths has shown that M-Shell multiple ionization

does accompany the L-Shell ionization process. However, no

double L-Shell ionization was observed. In the absence of

multiple L-Shell ionization, the Coster-Kronig rates should

remain essentially constant. Also, the fluorescence yields

have been shown to be constant for up to six M-Shell vacancies

for elements with Z>29 by Fortner et al.87 While L- or M-Shell

multiple ionization or both is likely to some degree for 7Li3

ionization with decreasing probability for 4He and 1H

48

ionization, its effect on the observed x-ray production

cross sections should be significantly less than observed

16for 80 ionization.

In order to observe the effects of the inclusion of

the individual contributions of the binding energy and

Coulomb deflection modifications to the PWBA, Figure 10

compares the PWBA-B and the PWBA-C to the H ion, He ion,1 n, 2 Heinand 7Li ion data for 7 0Yb. For the La cross sections,3 701,2

the PWBA-B fits the data well for 4He and 7Li ions but

overestimates the cross section for proton ionization. The

PWBA-C tends to overestimate the magnitude of the cross

sections for all ions. However, at energies below 0.5

MeV/amu, the PWBA-C does fit the data better than the PWBA-B.

The LyI and LY2 ,3 ,(6 ) x-ray production cross sections

shown in Figure 10 on the other hand are better fit by the

PWBA-C. From Figure 10 one observes that the PWBA-B pre-

dicts a shift in the LY2 ,3,(6 ) shoulder to higher E/M values.

This shift is due to the increased binding energy of the

L1 subshell electrons which shifts the node of the 2s

velocity distribution to higher velocities. This shift

has just not been supported by data.12,1 7 ,2 2 ,84,88 Pepper8 4

suggests that a better velocity distribution might result

from the proper weighting of velocity distributions due to

effective Z numbers from Z2 to Z1 +Z 2. This would not move

the 2s nodal point but would increase the value of the

velocity distribution at that point.

Ions on 7Yb

.. o 2He

-7

-~ 3 .L*- --

-Ly

- - - -W-

10 1

100

100

lo

10

10 0

16 1

102

IQ-32 IL- I-f-IL--.I.LIV4I- II .-1441 1 1i1-0 10 2.0 3.0 4.0

E/M (MeV/omu)

Figure 10

49

LX(b)

--- L3

-I- ----- PWBA -C

50-.- I -

r

-Mm

so

An analysis of the Lac 1 2 /LY2 ,3,( 6 ) ratio (dominated by

the L3/L ratio) is shown in Figure 11 for 1H, He, and 7 Li

ions incident on 62Sm, 7 0Yb, and 82 Pb. Both the PWBA and

PWBA-BC have some difficulty predicting the proper magnitude.

However, the PWBA-BC (due to the inclusion of the binding

energy effect) predicts a shift in the peak of the La12

LY2,3, (6)ratio which is not supported by the data. This

PWBA-BC predicted shift increases as the incident ion atomic

number increases as shown in Figure 12. This figure shows

the ratio of the La 1 2/LY2 ,3,( 6 ) cross sections as predicted

by the PWBA and the PWBA-BC for 1 HHe,and Li ions on1 2 3

6 2 Sm in the energy range of 0.4 to 3.0 MeV/amu. Note that

the PWBA and the PWBA-BC begin to converge at higher energies

as expected. Figures 13 and 14 show the aLo /a and7 1a,2 Ly2 3the aLY Lc2,3 ratios for 7Li ions incident on 58Ce, 6 0Nd,

66 Dy,and 6 7 Ho in the energy range of 2.0 to 4.8 MeV/amu.

In this energy range which is well above the energy of the

L related cross section shoulder, both the PWBA and the

PWBA-BC fit the data within experimental error as expected

from the trend shown in Figure 12. Thus, no real evaluation

of the modifications to the PWBA can be made on the data

shown in Figures 13 and 14 alone.

Figure 15 shows the ratio of the a L L cross sections1 4 71 2

for H, 4He, and 7Li ion bombardment of 62Sm and 8 2Pb. These

ionization cross sections aL and aL were obtained by using

' I 1' TI ' I

F 62 Sm

4 He- /2

'.. ....7-.. i

7 Yb

*0 ~/ 0

He

- ... 2Li

O000O *0 0

R=i 2.Lrl--- L-- 3 ( 6 )

PWBA

PWBA-BC

OR

1Pb --8 2 P

H

4He

9 .00000. 0*

7 L3 Li

.,0.00,o .0 **~*

10 L2 LO 1 2.6 0.2 LO 1.8 2.6

E/M (MeV/amu)

Figure 11

51

I.. 'j I J

10

102

102

I x I

52

U

Ions on 6 2Sm

Ly2 ,3 ,(6 ) PWBA

-- PWBA-BC

10 2

7Li

R

10 2

2He

10 2

H

0.4 0.8 1.2 1.6 2.0 2.4 2.8

E/M(MeV/amu)

Figure 12

53

a

40 aLa1 ,2

a2,3 PWBA

30 -- PWBA-BC

20

3Li on 58Ce

40

30

20

73Li on 6 NdR

3 6

40

30

2 0 7 L n D3Lion66

40

300

70

3 Li on 6 7Ho

2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8E/M(MeV/amu)

Figure 13

I

wo

2

3

2

1

2.4 2. 3.2 3.6 4.0 4.4

E./M(eV/anu)

Figure 14

4.8

54

L-yR =

2L " 2-3- - - - -P W B A

- PWBA-BC

3 Li on 5 8Ce

3Li on Nd3 60

7..

3 66

7

3 Li on 6 7Ffo.. tt

R

3.

2.

2.. U1

40

R =

L2

1H

4He

o 7Li

R for 6 2Sm

R for 8 2Pb

.,.. .."A

I *- -. -m-_.3.0 4.0

E/M(MeV/amu)

Figure 15

55

R

.01- 4

A

1 ""

.1..o 2.0 5.0

PWBA( H, 4 2He , 3Li)

4HePWBA- BC (2He)

PWBA-BC( 3Li)

1 am

4m

...... w

do

56

the experimental x-ray production cross sections in Eqs.

IV-1 to IV-4. The data is compared to the PWBA and PWBA-BC.

Again it is observed that the PWBA best predicts the shape

as well as the magnitude of this ratio. The PWBA-BC again

predicts the shift of the minimum to higher energies.

Figure 16 illustrates the Z normalized ratio of the1

La1,2 x-ray production cross sections for 1H and He and

1 71H and 7Li ions on Yb. This data is compared to the PWBA,1 3 70

PWBA-B, PWBA-C, and the PWBA-BC. The PWBA-BC best fits the

data, however, it is very important to notice that the

PWBA-C predicts the correct shape of the ratio while the

PWBA-B predicts an inflection in the opposite direction.

Therefore, the PWBA-B does not appear to be consistent

with the 2He/1 H data. Since the 3Li/ 1IH data does not

extend below 0.9 MeV/amu (which corresponds to vl/vL=0. 2 1),

it is impossible to determine if this is also inconsistent

with the PWBA-B prediction. Here v1 is the ion velocity

and vL is the L-Shell orbital velocity.

Figures 11, 15, and 16 point out the significance in

studying ion-induced L-Shell phenomena in the energy range

that includes the point where the incident ion velocity is

0.19 times the L-Shell orbital electron velocity; i.e.,

v /vL=0.19 . This point is where the L1 associated cross

sections begin to exhibit the shouldered structure and

Ratios for Ions on 70Yb

a (3Li)La 1 2

1,2

S .... in~-t -. - m--- PWBA

- - PWBA-B

- - PWBA -C

..m...PWBA-BC

y a 2He)

R La1 92(H

1,2

-.- "

aTo .eOlse z"Em

0.4 0.8 1.2 1.6 2.0

E/M(MeV/amu)

2.4 2.8

Figure 16

57

1.84,

1.4+

N1.0

0.61

0.24

R I

1.8"t

1 .004..- I

0.6.

0.2 B I S-- -___------ I

.a

a

W.

4

01

4

I &

58

where the theory (with its use of hydrogenic wavefunctions)

experiences the greatest difficulty in predicting the data.

Figure 17 shows the Lal,2 x-ray production cross

sections for 7Li ions on 58Ce, 60Nd, 62Sm, 6 6Dy, 67Ho,

70 Yb,and 82Pb in the energy range of 0.9 to 4.4 MeV/amu.

This figure simply illustrates that cross sections for a

given incident ion (Z1 ) decrease as the atom number of the

target.(Z 2) increases.

M(c14 0400

(n~

0*04

GeI)

4((34401444

4 4i a4. 4

44

444

I''"4

a44

4

44

444

1010

o00000000

q 04 04 0

44 04 04 0

44 044 04 4 0

4 44 4

I

a*u0

59

H431c

.

Eota*

*

'0 4

0"V44J0

t44A

0

0104

C"-4

H

0

V4

94

00

- ____________J_ _*$______1-_n -

------- 4--J 4__iu._1__sunr uI I

-

a

.a

4

-a

q

CHAPTER V

CONCLUSIONS

L-Shell x-ray production cross sections have been

measured for 1H,4 He,and 7Li ions incident on selected1 2He, 3L

target elements from 58Ce to 82Pb over a wide range of

incident ion energies. The x-ray production cross sections

and their ratios as well as the vacancy production cross

sections associated with these x-ray production cross

sections have been compared to the PWBA and the PWBA with

binding energy and/or Coulomb deflection effects. The

PWBA and the modified PWBA theories fit the data within

about 25% for values of vl/vL>0.19. Although the PWBA-BC

best fits the La 1,2 (associated with the L3 ionization

cross section) data in this vl/vL range, the PWBA best

fits the Ly1 and Ly 2 ,3 ,(6 ) (associated with the L2 and L

ionization cross sections, respectively) data. It is also

important to note that the PWBA does predict the proper

Ly2 ,3,(6) (2s related) shouldered structure for all target-

incident ion systems studied while the PWBA-BC predicted a

shift to higher ion velocity values. A study of the

individual contributions of the Coulomb deflection and

binding energy effect to the PWBA predictions indicated

60

61

that the binding energy modification predicted a shift in

the L1-associated data to higher E/M values which is not

consistent with existing data. The PWBA-C does properly

predict the shouldered structure of the L -associated

data.

Under the assumptions that the polarization effects

[which are of the order of (Z1 /Z2) 3], the electron capture

effects [which are of the order of (Z1 /Z2 ) 5, and the

relativistic effects are small, then the problems exhib-

ited by the PWBA and modified PWBA in properly predicting

the data might be expected to be due to one or a com-

bination of the following reasons. First, the wavefunctions

used to describe the atom might not be sufficiently accurate.

Second, the method in which the binding energy and Coulomb

deflection effects are incorporated into the theory might

be too simplified. Finally, the uncertainties of the

radiative and nonradiative parameters used to calculate

the theoretical cross sections might be very large.

One can conclude that the discrepancy between theory

and data is not due to the last reason stated above, since

the discrepancy between the theory and data appears to be

energy dependent, while evidence exists showing that these

radiative and nonradiative parameters do not appear to be

greatly dependent upon energy. However, it should be men-

tioned that Chen et al. 89 have observed large discrepancies

62

between the theoretical and measured Coster-Kronig transitions

for silver and have suggested that the theory of the Coster-

Kronig transitions be reexamined.

It must also be remembered that the PWBA and the modified

PWBA make use of screened hydrogenic wavefunctions which do

not take into account the presence of other electrons except

through the effective screening factor. It is well estab-

lished that the PWBA has difficulty predicting the low energy

L-Shell phenomena (See for example Ref. 13-27). The method

in which the Coulomb deflection modification is applied

withstands the test of predicting the L1 related cross section

structure. However, the method in which the binding energy

modification is applied does not properly predict the L

structure. This is a direct consequence of the shift of the

node in the 2s velocity distribution due to the increased

binding energy experienced by the electrons. The problem

with the binding energy correction could be due to the fact

that Brandt and Lapicki47 chose the semi-classical approxi-

mation (SCA) ionization probability functions in their

impact parameter formalism of the low velocity limit which

yielded monotonically decreasing functions with increasing

impact parameters. Stiebing et al.14 have measured the

impact parameter for Pb and found that in the low velocity

limit, the BEA best predicted the ionization probability.

Pepper has also suggested that a better method of including

63

the binding energy effect might be to calculate the modified

velocity distribution by properly weighting the velocity

distributions due to effective charges ranging from Z1to

z1 +Z2 Overall, the PWBA and PWBA-BC do predict the L-Shell

phenomena reasonably well with the exception of the L sub-

shell related phenomena.

Several models have been used to describe the ion-atom

collision process. The screened hydrogenic model (for

example, the PWBA) uses hydrogenic wavefunctions to describe

the target electron involved in the collision but does not

directly consider the presence of other atomic electrons.

This use of hydrogenic wavefunctions might be the cause of

the discrepancy between the theory and the data. The Hartree

Fock model90 does include the presence of the other electrons

in the atom and should inherently be more accurate. However,

this model requires numerical methods to solve the integrals

in order to obtain the first Born term. Basbas et al.46 have

pointed out that the Hartree-Slater method and the screened

hydrogenic (PWBA) method differ only slightly for the K-Shell

processes. This explains the success of the PWBA in predicting

the K-Shell phenomena even though the more rigorous Hartree

Slater method should be more accurate. However, the dif-

ferences for the L-Shell related phenomenal between these

two approaches could be large. Recently, Ford et al. 51

developed a numerical semiclassical approach for the K-Shell

64

using a wavefunction that is expanded in a truncated set of

Hilbert functions. Ford found that his method was easy to

apply using a one centered expansion of the time dependent

potential. Future work along similar lines should be con-

ducted for the L-Shell.

In summary, this work has shown that the PWBA and the

modified PWBA can be expected to predict ion-induced L-Shell

processes reasonably well for ZI<<Z2 and for incident ion

velocities such that vl/vL is above 0.19. The binding energy

modification to the PWBA has difficulty in predicting the

proper shouldered structure of the L1 -associateddata. This

could be due to the use of SCA ionization probabilities for

the low velocity limit of the PWBA. However, this is not

in agreement with the work of Stiebing.16 Thus, the binding

energy effect should be reexamined. Furthermore, the use of

screened hydrogenic wavefunctions may not provide a suffi-

ciently accurate description of the target atom. Although

the use of other wavefunctions also provide sources of

discrepancy as well as being more difficult to use, theo-

retical work using a formalism similar to Ford et al.51 for

the K-Shell should be pursued for the L-Shell in order to

determine the net improvement, if any, in ability of theory

to predict data. Finally, future experimental work should be

concentrated in an incident ion energy region that brackets

the ion-target velocity ratio v1 /v2 s :*19.

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71

TABLE I

EXPERIMENTAL X-RAY PRODUCTION CROSS SECTIONS

1H Ions on Yb1 70

1zAT( v)amu

Energy

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1 .1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

Lab)

5. 2x10-3

2.3x10-2

5.5x10-2

1 .0x10 1

1. 7x10 1

2. 5x101

3.4x101

4.4x10 1

5. 6x10'

6.4x10'

8.6x10 1

1.0

1.2

1.3

1.5

1.7

1.8

1.9

2.2

2.7

2.8

3.0

a Lk error is 10%

b Lot,2 error is 9%

c

d

L y error is 14%

Ly2 ,3 error is 14%

La 1)2b(b)

1 .1x10 1

4 .6x10 1

1.1

2.1

3.4

5.0

7.1

9.5

1. 2x101

1.4x101

1.9x101

2.2x10 1

2.5x10 1

2 .3x101

3.2x101

3. 5x101

3.9x101

4.1x101

4.5x1 01

5.4x101

5.5x101

5.8x101

Lyc (b)

7.7x10 3

3.0x10-2

7.3x10-2

1.4x10~1

2 .3x10 1

3.5x10 1

5 .0x10 1

5.7x10 1

6. 7x101

1.0

1.4

1.7

1.9

2.2

2.5

2.8

3.2

3.3

3.7

4.4

4.5

4.8

Ly2 , 3 (b)

6.7x10-3

1 .8x10-2

3.1x10-2

4.2x10-2

5 .1x10- 2

5.9x10-2

8 xO-27 .40x10~

1 .xlO -1.5x10~

2 .0x101

3.Oxl0~

3.2x10 1

4 .4x10-

5.5x10~

6. 7x10 1

8. 5x10~

8. 7x10 1

1.1

1.3

1.5

1.6

72

TABLE I--Continued

H1Ions on 82Pb

Energy (M ) Lk a (b) Lot, 2 b (b) by1 c (b) LY2 3(6) d(b)

5.0x10-3

1 .5x10 -2

2 .9x10-2

5 . 0x10-2

7.8x10-2

1 .0x10

1.4x10~

1 .8x10~

2. 3x10~

2. 7x10~

3.lxl0~

3. 7x1O-

4. 3x10~

4 .9x10

5.6x10 1

6.4x10 1

7 .3x10

8.0x10~

8 .6x10~

8.0x10-2

2 .4x10 1

4 .8x10 1

8 .3x10 1

1.2

1.8

2.4

3.1

3.8

4.6

5.5

6.4

7.5

8.6

9.9

1.1x10'

1 . 3x101

1.4x101

1 . 5x101

3. 2x10-3

1 .1x10 -2

2. 2x10 -2

4. 1x10-2

6 .3x10-2

9 .3x10-2

1.3x10 1

1.7x10~ 1

2.1x10~1

2 . 7x10 1

3. 3x10~

4 .0x10 1

4.7x10~

5. 5x10~

6.4x10'

7 .4x10 1

8 .3x10 1

9.4x10 1

1.0.

2 .9x10-3

7. 2x10-3

1. 3x10 -2

1 .8x10-2

2 .4x10-2

3.0x10-2

3.6x10-2

4.4x10-2

5.0x10-2

6 .1x10 - 2

7 .3x10 -2

8.1x10-2

9.6x10-2

1 .1x10 1

1 .3x10 1

1.6x10 1

1 .8x10-1

2.1x10-

2 .3x10 1

error is 10%

b Lot, error is 9%

c

d

Ly1 error is 14%

Ly2 ,3,(6) error is 14%

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

a

73

TABLE I--Continued

4He Ions on 62Sm

Energy (am) La (b) Lal1)b (b) Ly C (b) Ly 2,L 3 , ( 6 ) d (b)

0.15 3.1x10-3 8.5x10-2 1.1x10-2 9.5x10-3

0.20 1.4x10 - 2 3.8x10 4.3x10 - 2 3.2x10- 20.25 3.6x10-2 9.6x10' 9.5x10-2 5.8x10-2

0.30 7.2x10-2 2.0 2.0x10~ 9.6x10-2

0.35 1.2x10 1 3.4 2.9x10~1 2.9x10~ 1

0.40 1.8x10 1 5.1 4.7x10~ 1 1.6x10 ~0.45 2.6x10 1 7.2 6.4x10~1 1.5x10~1

0.50 3.6x10 1 9.9 9.1x10~1 2 .1x10~ 1

0.55 4.3x10' 1.3x101 1.2 2.0x10 1

0.60 5.8x10 1 1.6x10' 1.2 1.7x10 1

0.8 1.8 4.5x101 3.1 3.9x10~1

0.9 2.5 5.9x101 4.1 5.3x10 1

1.0 3.2 7.6x101 5.3 8.0x10 1

1.1 3.9 9.3x101 6.6 1.21.2 4.6 1.2x10 2 8.1 1.4

1.3 5.1 1.4x102 9.9 2.21.4 6.7 1.6x102 1.2x10 2.9

a L error is 10%

b La,2 error is 9%

c

d

Ly1

error is 14%

Ly 2 ,3,(6) error is 14%

74

TABLE I--Continued

4He Ions on 62Sm

Energy (u) La (b) Lot 1 2b(b) Ly1C(b) LY 2 3(6) (b)

1.5

1.6

1.7

1.8

1.9

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

7.5

8 * 8

9.6

1 .lxlO1 . 3x101

1 .4x101

1. 6x101

1. 8x10

2.0x101

2.2x101

2.6x101

2. 6x10

2.7x10

3. OxlO

2.8x101

3.5x101

3.8x10

3.9x101

1 .9x102

2.2x10 2

2 . 5x102

2. 8x10 2

3 . 1x10 2

3.4x10 2

3 . 7x10 2

4 . 5x10 2

5. 2x102

5. 3x102

6.8x10 2

6. 4x10 2

7.lxlO2

8. 2x102

7.7x10 2

8.6x10 2

9.7x102

9.9x10 2

1.4x101

1.6x101

1.9x101

2.lxlO

2 . 3x10'

2.5x101

2. 9x10'

3. 5x101

4.lxlO

4.2x101

5. 3x101

5.ox101

5.6x101

6.7x101

6.1x101

6 .9x10'

7.6x10'

7.9x101

3.7

4.9

5.5

7,.2

8.4

9.3

1 . 3x10

1 .6x10.x12 .OxlO

2.1x101

2.8x10

2 . 7x10

3.Oxl0

3.8x10

3.6x10

4.1x101

4. 7x10

4.9x10

a Lk error is 10%

b Lal,12error is 9%

c

d

Ly1 error is 14%

Ly 2 ,3, (6) error is 14%

75

TABLE I--Continued

4He Ions on 70Yb2 7

Energy (1) LZa2(b) L, 2b(b) Ly1 (b) Ly 2 ,3d(b)

0.30 3.9x10-2 7.2x10- 6.2x10- 4.1x10-2

0.35 7.7x10-2 1.3 1. -x 1 62x10-2

0.40 1.2x10' 2.2 1.7x10 1 8.0x10-2

0.45 1.8x10 1 3.2 2.4x10~ 9.8x10-2

0.50 2.4x10 1 4.4 3.3x10~ 1.2x10 1

0.55 3.0x10 1 5.8 4.lxlO-1 1.3x10 1

0.60 4.3x10 -1 8.1 5.9x10 -1 1.5x10~-1

0.8 9.5x10 1 2.0x101 1.3 2.2x10-1

0.9 1.3 2.6x101 1.7 2.4x10 1

1.1 2.1 4.3x101 2.9 3.5x10 1

1.2 2.8 5.5x101 3.7 4.9x10~

1.3 3.2 6.4x10 4.3 6.6x10 1

1.4 3.8 7.6x10 5.2 8.0x10 1

1.5 4.5 9.3x10 1 6.6 1.11.6 5.4 1.lxlO2 71.4

1.7 5.9 1.2x102 8.7 1.6

a Lk error is 10%

b Lot,2 error is 9%

c

dLy 1 error is 14%

Ly2 ,3 error is 14%

76

TABLE I--Continued

2He Ions on Yb

Energy (mu) Lka(b) Lo. 1 2b(b) Ly cb) Ly 2,3 d(b)au12 211.8 6.6 1.4x10 1.OxlO 2.11.9 7.3 1.5x10 2 1.1x10 2.32.0 8.1 1.7x10 2 1.2x10 3.02.2 9.2 1.9x102 1.4x10 4.02.4 1.2x10' 2.4x10 2 1.8x10 5.52.6 1.3x10 2.7x10 2 2.0x101 7.02.8 1.5x10 3.lxlO2 2.3x101 8.53.0 1.7x10 3.6x102 2.7x101 1.lxlO1

3.2 1.8x10 3.8x10 2 2.9x10 1.2x103.4 1.9x10 3.8x102 3.0x101 1.3x101

3.6 2.0x101 4.4x102 3.3x101 1.6x10

3.8 2.1x101 4.5x102 3.5x10 1.7x10

4.0 2.5x101 5.2x10 2 3.9x101 1.9x101

4.2 2.8x101 6.1x10 2 4.7x10 2.4x10

a Lk error is 10%

b Lot,2 error is 9%

c

d

Ly error is 14%

Ly2 ,3 error is 14%

77

TABLE I--Continued

4He Ions on 82Pb

Energy ( ) Lk' (b) La 2 b (b) Ly c(b) LY2 3 (6 )d(b)

0.30 8.7x10-3 1.1x10 1 9.3x10-3 5.4x10-3

0.35 1.8x10-2 2.9x10 1 1.9x10- 1.5x10-2

0.40 3.1x10-2 5.3x10 1 3.4x10-2 2.5x10- 2

0.45 5.1x10-2 8.6x10 6.2x10- 3.5x10-2

0.55 1.0x10 1 1.8 1.2x10 1 5.6x10-2

0.60 1.4x10 1 2.5 1.5x10 1 6.9x10-2

0.80 3.2x10~ 5.4 3.2x10' 1.2x10~

0.90 4.2x10~ 7.5 4.5x10 1.6x10 1

1.00 5.7x10 1 1.OxlO 5.9x10- 1.9x10 1

1.10 7.4x10~ 1.3x10 7.9x10~ 2.4x10~

1.20 9.0x10O 1.6x10 9.8x10 1 2.7x10~

1.30 1.1 2.0x10 1.2 3.1x10 1

1.40 1.4 2.4x10 1.5 3.8x10-

1.50 1.7 2.9x10 1.5 4.4x10~

1.60 2.0 3.5x10 2.3 5.9x10-

a Lk error is 10%

b Lot,2 error is 9%

c Ly1 error is 14%

d LY2 ,3 ,(6) error is 14%

78

TABLE I--Continued

2He Ions on 82Pb

Energy (MeV) La (b) (Lb(b) Ly c (b) LY 2 ,3(6) (b)

1.70 2.3 4.0x101 2.3 6.8x10-11.80 2.6 4.5x101 3.0 7.3x101.90 2.7 5.0x101 3.2 8.4x10 -1

2.00 3.1 5.9x10' 3.9 1.12.20 3.8 6.7x101 4.6 1.22.40 4.5 8.1x101 5.7 1.52.60 5.3 9.8x10' 6.9 2.02.80 6.4 1.2x10 2 8.4 2.53.00 7.4 1.4x102 9.5 3.03.20 8.0 1.5x102 1.OxlO 3.73.40 9.1 1.7x102 1.2x10 4.23.60 9.6 1.8x102 1.3x10 4.73.80 1.lxlO 2.OxlO2 1.4x10 5.24.00 1.1x101 2.lxlO2 1.4x10 5.84.20 1.2x10 2.3x102 1.6x10 6.64.40 1.9x101 2.6x10 2 1.9x101 7.7

a Lk error is 10%

b Lal,2 error is 9%

c Ly1 error is 14%

d LY2,3, (6)error is 14%

79

TABLE I--Continued

7Li Ions on 58Ce

Energy ( ) LPa (b) Lal, 2b(b) Ly c (b) Ly2 d(b)

3 12.0 4.6x10 1.2x10 3 7.0x10 3.7x10

2.2 5.7x101 1.4x10 3 8.3x101 5.2x10

2.4 6.5x101 1.6x10 3 9.9x10 5.8x101

2.6 6.7x101 1.9x103 1.1x102 6.2x101

2.8 7.9x10 2.2x103 1.3x102 7.8x101

3.0 8.7x10 2.2x10 3 1.3x102 8.9x101

3.2 9.lxlO1 2.SxlO3 1.5x102 1.Ox12

3.4 1.Ox12 2.9x103 1.8x102 1.2x102

3.6 1.2x102 2.9x103 1.8x102 1.3x10 2

3.8 1.2x102 3.lxlO3 1.9x102 1.4x10 2

4.0 1.7x102 4.0x103 2.5x102 1.8x10 2

4.2 1.8x10 2 4.5x103 2.8x102 1.9x102

4.4 1.7x102 4.2x10 3 2.5x10 2 1.9x02

4.6 1.9x102 4.3x103 2.8x102 2.1x10 2

4.8 2.1x103 4.8x103 3.1x10 2 2.4x10 2

a Lk error is 11%

b Lo,2 error is 10%

c Ly1 error is 15%

d Ly2 ,3 error is 15%

80

TABLE I--Continued

3Li Ions on 60Nd

Energy ( )j Lk')(b) Lot, 2b (b) Ly (b) Ly2 3 d(b)au1 2 Y1, 1

2.0 3.5x101 8.9x10 5.3x10 2.2x10

2.2 3.9x10 1.0x103 6.lxlO 2.8x10

2.4 4.6x10 1.2x103 7.0x10 3.5x10

2.6 5.7x101 1.4x10 3 8. 5x10 4.6x101

2.8 7.0x101 1.6x10 3 9.6x101 5.9x101

3.0 7.6x101 1.7x10 3 1.0x10 2 6.2x10

3.2 8. 1x10 1.9x10 3 1.2x10 2 6.9x10

3.4 9.2x101 2.1x103 1.4x102 8.3x103.6 1.1x10 2 2.3x10 3 1.5x10 2 9.6x101

3.8 1.2x10 2 2.6x103 1.7x10 2 1.1x102

4.0 1.1x10 2 2.8x103 1.8x102 1.lxlO24.2 1.4x102 3.2x103 2.0x10 2 1.4x10 2

4.4 1.4x102 3.1x103 2.0x102 1.3x10 2

4.6 1.6x102 3.3x103 2.2x102 1.5x10 2

4.8 2.1x102 3.7x103 2.7x102 1.7x102

a Lk error is 11%

b La,2 error is 10%

c Ly1 error is 15%

d Ly 2 ,3 error is 15%

81

TABLE I - -Continued

7Li Ions on 62Sm

Energy (-) Lk'(b) Lot,(b) LYc(b) L , d(b)amu 1)2(1Y2p()

0.8 4.2 8.7x10 5.8 8.7x10 1

0.9 5.6 1.1x10 2 7.7 1.2

1.0 7.4 1.6x102 1.0x10 1.7

1.1 8.5 1.8x102 1.2x10 2.3

1.2 1.0x10 2.2x10 2 1.5x101 3.0

1.3 1.2x10 2.6x102 1.8x10 4.2

1.4 1.5x101 3.0x102 2.lxlO1 5.6

1.5 1.7x10 3.6x10 2.5x10 7.0

1.6 2.0x101 4.2x10 2 3.0x101 9.0

1.7 2.2x10 4.9x102 3.4x101 1.2x101

1.8 52,.4x10 1 .3x10 2 3.7x10 1.4x10

1.9 2.8x101 6.0x10 2 4.3x101 1.7x101

2.0 3.0x101 6.5x102 4.6x10' 1.9x101

2.1 3.3x10 7.OxlO2 5 .lxlO 2.2x101

2.2 3.7x101 7.8x10 25 .7x10 2,.6x10

2.3 4.OxlO 8.6x102 6.3x10 3.OxlO

2.4 4.3x10 9.3x102 6.9x10 3.4x10

2.6 4.7x10 1.0x103 7.8x10 3.9x10

2.7 5.6x10 1.1x10 3 8.7x10 4.7x10

2.8 6.1x101 1 .3x10 3 9.9x10 5 .5x10

2.9 6.4x10 1.3x103 1.0x102 5.7x103.0 6.5x10 1.3x103 1.0x102 5.8x10

a Lk error is 11% c Ly1 error is 15%

b La,2 error is 10% Ly2 ,3 error is 15%

82

TABLE I--Continued

3 Li Ions on 66Dy

g MeV a b(b)--dEnergy (u) Ll(b) Lt 1 2 b(b) Ly1 (b) Ly23 (b)

12 112.0 3.6x10 5.5x10 3.4x10 1.3x10

2.2 3.8x101 6.0x10 2 3.7x101 1.4x101

2.4 4.5x10' 7.9x102 5.0x10 2.lxlO1

2.6 4.7x10 8.6x102 5.2x10 2.4x101

2.8 6.5x101 1. 0x103 6.7x10 3.2x101

3.0 6.4x101 1. 0x103 6.5x101 3.3x101

3.2 7.2x10 1.3x10 3 8.lxIO 4.5x10

3.4 7.0x101 1.4x10 3 9.2x101 4.9x101

3.6 8.5x10' 1.5x103 9.5x10' 5.6x101

3.8 8.3x101 1.5x10 3 9.7x101 5.9x101

4.0 1.0x102 1.8x103 1.2x102 7.4x101

4.2 9.lxlO1 1.7x10 3 1.2x102 6.9x101

4.4 1.Ox1O2 1.8x103 1.3x102 7.2x101

4.6 1.2x102 1.9x10 3 1.3x102 8.1x10 1

4.8 1.2x102 2.1x103 1.4x102 8.4x10 1

a Lk error is 11%

b Lot,2 error is 10%

c Ly1 error is 15%

d Ly 2,3 error is 15%

83

TABLE I--Continued

Li Ions on 67Ho

Energy ( ) La (b) La, (b) Ly1 c(b) Ly2 3d(b)amu 12 () L

12 13.0 4.5x10 9.2x10 5.8x10 2.7x10

3.2 5.2x101 1.1x10 3 6.8x10 2.9x101

3.4 5.9x10 1.2x10 3 7.5x10' 3.8x101

3.6 6.2x10 1.4x10 3 8.3x10 4.2x101

3.8 8.5x10 1.7x103 1.1x102 5.9x101

4.0 1.OxlO2 1.9x103 1.2x102 7.1x101

4.2 8.2x11. 8x10 3 1.lxlO2 6 .3x10

4.4 9.4x10 1.9x103 1.2x102 7.2x101

4.6 9.5x10 1.9x103 1.2x102 7.6x101

4.8 9.8x10 2.0x103 1.3x102 7.9x101

a Lk error is 11%

b La,2 error is 10%

c Ly1 error is 15%

d Ly2 ,3 error is 15%

84

TABLE I--Continued

Ions on 70Yb

MeV ab-cd-Energy (-) L (b) La~ (b) LyC(L) 2L (b)amu 1,2 12)3

3.4

4.6

5.4

6.7

8.0

9.5

1.1x101

1 . 3x101

1 .5x10'

1.8x101

2.0x101

2.2x101

2.3x10

2.7x10'

3.0x10

3. 3x101

3.8x101

4.Oxl0

4.7x101

5. 2x101

5. 7x1O~

7.1x10~

8 .2x10

1.0

1.3

1.6

2.1

2.7

3.3

4.1

4.9

6.0

6.8

8.0

9.8

1 . 2x101

1.5x101

1.6x101

2.0x101

2.3x101

a Lk error is 11%

b La,2 error is 10%

c Ly1 error is 15%

d Ly 2 ,3 error is 15%

7Li

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2. 2

2.3

2.4

2.6

2.7

2.9

3.0

2.5

3.4

4.2

5.2

6.2

7.2

8.4

9.8

1.1x101

1.3x101

1.4x101

1.6x101

1 .7x101

1.9x101

2.lxlO

2 .4x10'

2.8x10'

2.8x101

3.2x101

3.5x101

5.0x101

6.8x101

8. 2x101

1.0x10 2

1. 2x102

1.4x10 2

1. 7x102

2. 0x102

2 .3x102

2.6x102

2.8x10 2

3.2x10 2

3.3x10 2

3.8x102

4 .3x102

4 . 7x10 2

5 . 5x10 2

5 .7x102

6.6x10 2

7.1x102

85

TABLE I--Continued

7Li Ions on 82Pb

Energy ( ) LZa(b) Lot 2 (b) Ly (b) y 2,3 6 d(b)

8. 3x10 1

1.2

1.4

1.9

2.1

2.5

2.9

3.6

3.9

4.6

5.1

5.8

6.0

7.2

7.4

8.6

9.3

9.9

1.1x101

1.1x101

1.3x101

1.4x101

1.4x101

2.1x101

2.6x101

3.2x101

3.7x101

4 . 5x101

5.3x101

6.3x101

7.1x101

8.3x101

9.1x101

1.0x10 2

1.1x102

1 .3x102

1.4x10 2

1.6x102

1 . 7x1021 . 8x1 02

2.0x10 2

2.0x10 2

2.3x10 2

2.6x102

9. 2x10 1 2 .7x10~

1.3 3.6x10~

1.7 4.4x10 1

2.1 5.1x10

2.5 5.7x10 1

3.0 6.6x10~

3.5 7.9x10 1

4.2 9.2x10 1

4.8 1.0

5.6 1.3

6.2 1.4

6.9 1.7

7.5 1.8

8.9 2.0

9.5 2.3

1.xlO1 2.6

1.2x101 3.0

1.3x10 3.4

1.4x10 3.6

1.4x10 3.8

1.6x10 4.3

1.8x10 5.0

a Lk error is 10%

b Lot,2 error is 9%

c Ly1 error is 14%

d Ly2 ,3 ,6 error is 14%

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

86

TABLE II

EXPERIMENTAL X-RAY PRODUCTION CROSS SECTION RATIOS

H Ions on Yb70

MaIT

Energy ( V)amu

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

La 1,2/Lka Lo'2/LyIb La1 ,2/Ly2 ,3

21.8

20.4

20.7

20.5

20.5

20.4

20.7

21.5

20.9

21. 7

21.6

21.4

21.5

21 .7

21.7

20.9

21.9

21.2

20.6

20.3

20.1

19.6

14.9

15.3

15.4

15.0

14.8

14.6

14.3

16.8

17.5

13.5

13.4

13.1

13.1

12.8

12.8

12.6

12.4

12.4

12.4

12.3

12.3

12.0

17.1

25.4

36.2

49.3

66.9

84.8

96.3

119.4

114.7

94.5

92.5

74.6

77.7

63.3

58.6

52.5

46.0

47.4

43.7

40.8

38.2

36.4

Ly 1 /Ly2 3d

1.2

1.7

2.4

3.3

4.5

5.8

6.7

7.1

6.6

7.0

6.9

5.7

5.9

4.9

4.6

4.2

3.7

3.8

3.5

3.3

3.1

3.0

a Lc 12/Lk error is 13%

b La 1,2/Ly1 error is 17%

c La 1 ,2/Ly2 ,3 error is 17%

d Ly1 /Ly 2 ,3 error is 20%

87

TABLE II--Continued

H Ions on Pb1 82

Energy ( evamu

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

I T

a L.a,2 /Lkerror is 13%

bLol, 2/Ly1 error is 17%

c Lot,2/Ly2,3,6 error is 17%

dLy 1/Ly2 3 ,6 error is 20%

dLot,2/LP, La11 2/LY1 b L.1,2/Ly 2,3,6

15.8 25.1 28.0

15.8 23.1 33.7

16.7 21.8 37.7

16.6 20.3 46.9

16.0 19.9 52.2

16.7 19.0 59.4

16.9 18.5 64.7

16.8 17.5 69.8

16.7 17.7 75.8

16.8 16.9 76.0

17.5 16.5 75.7

17.2 16.2 79.4

17.3 15.8 77.9

17.5 15.7 78.0

17.8 16.6 75.0

17.7 15.3 73.2

17.3 15.2 71.4

17.7 15.0 67.8

17.5 14.7 67.2

Ly 1 Ly 2,3,6

1.1

1.5

1.7

2.3

2.6

3.1

3.5

4.0

4.3

4.5

4.6

4.9

4.9

5.0

4.8

4.8

4.7

4.5

4.6

88

TABLE II--Continued

42He Ions on 6 2 Sm

Energy (MeV) LV, a/LPaamu 1)

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.80

0.90

1.00

1.10

1.20

1.30

1.40

27.3

28.3

26.6

28.3

27.7

28.1

27.9

27.3

29.8

27.7

24.6

23.8

23.6

24.1

25.4

27.6

24.3

Lo 12/Ly 1b La 1 2/Ly2, 3

4.5

9.0

10.1

10.3

11.4

11.0

11.4

10.8

10.8

13.3

14.6

14.4

14.3

14.2

14 . 3

14.2

13.9

8.9

12.2

16.5

21.2

33.2

47.9

47.2

62.9

93.6

116.8

110.4

95.5

79.9

80.8

63.1

55.4

C Ly 1/Ly 2 ,3

1.1

1.3

1.6

2.1

3.0

4.2

4.4

5.8

7.0

8.0

7.7

6.7

5.6

5.6

4.5

4.0

a La, 2/Lk error is 13%

b Lot1 2 /Ly1 error is 17%

c La 1 2 /Ly 2 , 3 error is 17%

d Ly 1/Ly 2 ,3 error is 20%

d-w- --

89

TABLE II--Continued

4He Ions on Sm2 62

Energy (9 La, 2/Lka Lal2 /Ly b LcL 2/Ly2 aC Ly1/Ly23d

1.50

1.60

1.70

1.80

1.90

2.00

2.20

2.40

2.60

2.80

3.00

3.20

3.40

3.60

3.80

4.00

4.20

4.40

25.5

25.1

26.3

25.2

24.4

24.9

23.3

24.6

25.9

24.5

26.1

24.3

26.0

27.8

27.6

24.8

25.3

25.2

13.7

13.7

13.5

13.6

13.3

13.4

13.4

12.9

12.7

12.8

12.8

13.0

12.8

12.2

12.6

11 .5

12.6

12.6

51.5

45.4

45.5

39.8

37.1

36.6

27.9

28.3

26.2

25.1

23.7

23.8

23.5

21.7

21.4

20.9

20.8

20.2

3.8

3.3

3.4

2.9

2.8

2.7

2.3

2.2

2.1

2.0

1.9

1.8

1.8

1.8

1.7

1.7

1.6

1.6

Lo 1 2/Lk.

La,1 2/Ly 1

error is 13%

error is 17%

c La 1 , 2 /Ly 2 , 3 error is 17%

d Ly 1 /Ly 2 ,3 error is 20%

90

TABLE II--Continued

4He Ions on Yb2 70

Energy (-) La,/La La,/Lyb LoL 2/Ly2 3 C Ly1 /Ly2 3

0.30 18.4 11.6 17.9 1.5

0.35 17.2 12.2 21.2 1.7

0.40 18.0 13.0 27.1 2.1

0.45 18.0 13.1 32.7 2.5

0.50 18.3 13.4 37.8 2.8

0.55 19.4 14.1 43.7 3.1

0.60 18.7 13.7 53.6 3.9

0.80 20.8 15.0 91.2 6.1

0.90 20.2 15.0 105.3 7.0

1.10 20.2 14.9 121.2 8.0

1.20 20.1 14.8 113.8 7.7

1.30 20.2 14.9 98.0 6.6

1.40 20.3 14.7 94.8 6.4

1.50 20.4 14.0 88.3 6.3

a La 1,2/LZ

bLoa 1 ,2/Y

error is 13%

error is 17%

c La 1 2 /Ly 2 , 3 error is 17%

dLy1/Ly2,3 error is 20%

91

TABLE II--Continued

4He Ions on Yb2 70

Energy ( ) Lot ,/Lka La ,/Ly b Lot ,/Ly C Ly /Ly2,damu 1,2 1, 21 1122,3 L 1 L 213

1.60 20.5 14.2 80.2 5.7

1.70 20.9 14.1 75.0 5.3

1.80 21.2 13.7 66.7 4.9

1.90 20.3 13.8 64.4 4.7

2.00 21.1 14.0 57.4 4.1

2.20 21.1 13.9 49.0 3.5

2.40 21.0 13.5 43.7 3.2

2.60 21.3 13.4 38.8 2.9

2.80 21.0 13.4 35.7 2.7

3.00 21.4 13.1 32.8 2.5

3.20 20.0 12.5 29.1 2.3

3.40 20.6 13.0 29.0 2.2

3.60 21.5 13.2 27.9 2.1

3.80 21.3 12.9 26.6 2.1

4.00 20.9 13.1 26.7 2.04.20 21.8 12.9 25.0 1.9

L.1,2/L error

La,2 /Ly1erro

is 13%

r is 17%

c La 12/Ly2 ,3 error is 1

d Ly 1/Ly2 ,3 error is 20%

7%

92

TABLE II--Continued

4He Ions on 82Pb

Energy ( ) Lot, 2/La La,/Ly b Lo 2/Ly 2 36 c LY/Lyd

0.30 12.3 11.6 19.8 1.7

0.35 15.4 14.8 18.7 1.3

0.40 16.8 15.5 21.2 1.4

0.45 17.0 14.0 24.4 1.8

0.55 17.5 15.6 32.8 2.1

0.60 17.7 15.9 35.4 2.2

0.80 16.3 16.9 45.1 2.7

0.90 17.6 16.7 48.2 2.9

1.00 17.4 16.8 52.6 3.1

1.10 17.5 16.3 54.6 3.4

1.20 17.8 16.4 60.0 3.7

1.30 18.5 15.8 63.0 4.0

1.40 17.6 15.5 62.5 4.0

1.50 17.4 19.4 66.0 3.4

a Lal,)2 /Lerror is 13% c La 2/Ly2 ,3 ,6 error is 17%

b dLcl, 2/Ly1 error is 17% Ly 1/Ly2 3,6 error is 20%

93

TABLE II--Continued

4He Ions on 82Pb

Energy (MeV) Lo 2/Lka La,/Ly b La/Lyc Ly /Lyd

17.2

17.6

17.7

18.3

18.9

17.7

18.1

18.6

18.5

18.3

18.8

18.3

19.3

19.2

18.9

18.9

18.5

15.2

17.9

15.2

15.5

15.0

14.3

14.3

14.1

14.0

14.3

14.4

14.1

14.2

14.4

14.5

14.3

14.0

59 .7

63.7

62.3

59.5

56.2

55.6

52.3

45.3

46.5

44.4

41.0

39.3

39.5

38.5

35.7

35.0

30.1

3.9

3.6

4.1

3.9

3.8

3.9

3.7

3.2

3.3

3.1

2.9

2.8

2.8

2.7

2.5

2.5

2.2

error is 13%

Lal 12/Ly error is 17%

c La,2 / Ly2,3,6error is 17%

d Ly/Ly2 ,3 ,6 error is 20%

1.60

1.70

1.80

1.90

2.00

2.20

2.40

2.60

2.80

3.00

3.20

3.40

3.60

3.80

4.00

4.20

4.40

a Lal,2/L P

94

TABLE II--Continued

3Li Ions on 58 C

Energy (V) La. 2/Lka La,/LY b La,/LYc Ly/Lyd

2.0 25.6 17.0 3.25 1.9

2.2 14.9 17.2 27.5 1.6

2.4 24.6 16.1 27.5 1.7

2.6 28.5 17.9 31.0 1.7

2.8 27.4 16.7 27.7 1.7

3.0 25.1 17.4 25.9 1.5

3.2 27.5 16.6 24.3 1.5

3.4 29.2 16.8 25.4 1.5

3.6 23.9 16.2 22.3 1.4

3.8 26.0 16.5 22.3 1.4

4.0 24.2 15.9 22.2 1.4

4.2 25.6 16.2 23.2 1.4

4.4 23.9 16.3 21.9 1.3

4.6 22.7 15.8 21.2 1.4

4.8 23.3 15.5 20.2 1.3

a Lal,)2 /Lerror is 15%

b La 1 2/Ly1 error is 18%

c La 12/Ly2 ,3 error is 18%

d Ly 1 /Ly 2 ,3 error is 21%

95

TABLE II--Continued

3Li Ions on 60Nd

Energy ( )M Lo.,/Lk9a La 2/Ly bLa 2/L 2 3 Ly/Ly2 3

2.0 25.0 16.9 39.5 2.3

2.2 26.6 17.0 37.5 2.2

2.4 35.7 16.6 33.5 2.0

2.6 23.7 16.1 29.4 1.8

2.8 22.5 16.4 26.5 1.6

3.0 21.9 16.1 27.3 1.7

3.2 23.0 15.6 27.2 1.8

3.4 23.8 15.3 25.1 1.6

3.6 20.7 15.3 23.6 1.6

3.8 22.0 15.5 23.9 1.5

4.0 25.5 15.4 25.2 1.6

4.2 22.1 15.6 23.2 1.5

4.4 21.2 15.3 23.4 1.5

4.6 20.2 14.9 22.4 1.5

4.8 17.2 13.7 21.7 1.6

error is 15%

Lal1,2/Ly1 error is 18%

c Lo 12/Ly2 ,3 error is 18%

d Ly 1/Ly 2 ,3 error is 21%

a Lal,2

96

TABLE II--Continued

Li Ions on 62Sm

Energy (e) Lt/L1,2/ a La ,/Lyb Lot,/Ly C Ly/Ly d

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.6

2.7

2.8

2.9

3.0

20.5

20.4

20.9

20.9

21.1

21.2

20.9

20.6

21.2

22.1

22.0

21.4

22.0

21.2

21.2

21.6

21.5

22.0

20.1

21.4

20.7

20.2

15.0

14.8

15.0

14.8

14.9

14.6

14.5

14.4

14.3

14.3

14.3

13.9

14.2

13.8

13.7

13.6

13.5

13.4

13.1

13.1

12.9

13.1

100.0

96.6

89.6

77.7

72.4

61.8

54.2

51.1

46.6

42.1

38.3

35.6

34.6

32.2

30.2

29.1

27.6

26.5

24.3

23.6

23.5

22.8

6.7

6.6

6.0

5.2

4.9

4.3

3.7

3.6

3.3

3.0

2.7

2.6

2.4

2.3

2.2

2.2

2.1

2.0

1.9

1.8

1.8

1.7

error is 13%

error is 17%

c La 1 2 /Ly 2 , 3 error is 17%

dLy1/Ly2,3 error is 20%

a Lot ,2/Lc

b La 1, 2/Ly 1

97

TABLE II--Continued

7Li Ions on 6 6Dy

MeV .a Lb1 Ly2Energy ( -u) Lot 1,2/Lka Lo 1 2/Ly 1 Lo 2 2,/Ly 2 3C Ly/LY2,3d

2.0 15.2 16.3 41.6 2.5

2.2 15.7 16.4 41.9 2.62.4 17.7 15.8 37.5 2.4

2.6 18.4 16.7 35.6 2.1

2.8 15.9 15.5 32.2 2.13.0 16.1 15.6 30.5 2.0

3.2 17.2 15.3 27.7 1.8

3.4 20.0 15.2 28.5 1.9

3.6 17.0 15.2 25.8 1.73.8 17.9 15.3 25.0 1.6

4.0 18.2 15.2 24.9 1.6

4.2 18.9 14.7 25.0 1.74.4 18.2 14.7 25.5 1.74.6 16.4 14.9 23.6 1.6

4.8 17.7 14.7 25.0 1.7

error is 15%

La 1,2/Ly1 error is 18%

c Lal, 2 /Ly 2 , 3 error is 18%

d Ly 1/Ly 2 ,3 error is 21%

a L /

98

TABLE II--Continued

7Li Ions on 67Ho

Energy ( ) Lot,2/LZa Lot2/Ly l La1,2/Ly2,3 Ly1/Ly2

3.0 20.2 15.9 34.2 2.23.2 21.5 16.3 37.7 2.33.4 20.3 15.9 31.3 2.03.6 21.7 14.7 32.1 2.03.8 20.2 15.9 29.1 1.84.0 19.5 15.9 27.4 1.74.2 21.8 16.4 28.3 1.74.4 20.5 15.7 26.8 1.74.6 20.2 15.5 25.4 1.64.8 20.4 15.4 25.3 1.6

La 1,2/Lk error is 15%

Lot 1 ,2/Ly1 error is 18%

c La1,2/LY2,3error is 18%

d Ly1 /Ly2,3 error is 21%

99

TABLE II--Continued

7Li Ions on 70Yb

EL ,2/ L a ,b L , LEnergyaMVLa'1)2Lk La 1)2/Ly L 1it2/Ly 2)3 cLy 1/Ly2 2 3 d

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.6

2.7

2.9

3.0

20.3

20.0

19.6

19.7

19.6

19.8

19.8

20.2

20.3

19.5

19.8

20.4

19.6

20.2

20.2

19.7

19.8

20.1

20.8

20.3

14.7

15.0

15.1

15.2

15.1

15.0

14.9

14.9

14.7

14.5

14.5

14.5

14.6

14.1

14.3

14.2

14.2

14.2

14.1

13.7

87.3

96.5

99.9

100.0

93.1

90.4

81.1

74.7

69.4

62.2

58.5

54.3

49.2

47.3

43.7

40.1

37.3

35.4

32.9

31.1

5.9

6.4

6.6

6.6

6.2

6.0

5.4

5.0

4.7

4.3

4.0

3.8

3.4

3.4

3.0

2.8

2.6

2.5

2.3

2.3

error is 13%

La 1.,2 /Ly error is 17%

c La 1 2 /Ly 2 ,3 error is 17%

d Ly1/Ly 2 ,3 error is 20%

aLLtl,2/Lk

100

TABLE II--Continued

7Li Ions on 82Pb

Energy (vV)amu

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

RA r% I

Lt 1 ,2/Lka

17.3

17.6

17.9

17.5

18.0

17.9

18.2

17.7

18.3

18.1

18.0

17.9

18.4

18.2

18.6

18.1

18.6

18.3

18.0

18.6

18.1

18.6

a Lo 1 2 /Lk error is 13%

b Lal 12/Ly1 error is 17%

c

dLa.2 /Ly2,3,P6error is 17%

Ly 1/Ly 2 ,3 ,6 error is 20%

I I - T r 4 -9

Lt 1 ,2/Ly 1

15.6

15.4

15.1

15.4

15.3

15.0

15.1

15.1

14.9

14.9

14.7

14.9

14.7

14.7

14.5

14.6

14.2

14.3

14.2

14.1

14.3

14.0

b LL22,3,6

52.7

57.4

59.0

63.3

65.6

67.7

80.0

68.3

68.7

63.7

66.0

60.9

60.8

65.2

59.7

59.5

58.7

54.0

56.3

53.3

53.9

50.9

cLy1/Ly2 3 ,6

3.4

3.7

3.9

4.1

4.3

4.5

4.4

4.5

4.6

4.3

4.5

4.1

4.2

4.4

4.1

4.1

4.1

3.8

4.0

3.8

3.8

3.6

101

TABLE III

RADIATIVE AND NONRADIATIVE RATES USED IN THE

THEORETICAL CALCULATIONS FOR THIS WORK

58Ce 60Nd 625m 66Dy 67 70Y82

0.069

0.119

0.122

0.198

0.293

0.152

0.244

0.017

0.027

0.413

0.060

<.001

0.385

0.012

0.283

0.032

0.075

0.133

0.135

0.207

0.303

0.141

0.289

0.021

0.033

0.492

0.073

<.001

0.456

0.015

0.334

0.038

0.085

0.153

0.154

0.206

0.305

0.140

0.333

0.024

0.037

0.568

0.080

<.001

0.524

0.017

0.386

0.044

0.107

0.193

0.192

0.203

0.308

0.139

0.464

0.035

0.052

0.797

0.121

<.001

0.727

0.021

0.529

0.060

0.112

0.203

0.201

0.202

0.309

0.138

0.499

0.038

0.056

0.859

0.131

<.001

0.782

0.021

0.569

0.065

0.113

0.239

0.230

0.199

0.319

0.132

0.608

0.047

0.066

1.051

0.154

<.001

0.947

0.034

0.693

0.078

0.116

0.402

0.374

0.072

0.653

0.109

1.349

0.117

0.139

2.378

0.383

0.047

2.060

0.085

1.438

0.163

*Reference 85

**Reference 86

*w

*W3

*y2

*y3

*f2

**P2Y

2y1

2y6**3 Y,

*3a1

32

APPENDIX

The relationships between the x-ray production cross

sections and the L-subshell ionization cross sections were

presented in Eq. IV-1 through Eq. IV-4. The purpose of this

appendix is to show that for the elements and energy range

considered in this work, a Lal2is dominated by aL3'aLy,

is dominated by aL2, and aLY2,3 is dominated by aL '

For all targets considered, w 2 2Y6/P2 is less than .01

and is therefore negligible. Thus from Eq. IV-4 it is

immediately obvious that aLy 2,3is dominated by aL '

From Eq. IV-3, one can write

KaLy1 = aL2 + f1 2 1(A-1)

where K is w2Pr2y1/2* Dividing Eq. A-1 by aLY the following

expression is obtained:

L LK 2 + f 1 (A-2)

Ly1 Ly

For all the target materials considered in this work, f is12-

less than 0.207. GL Ly and aL LYfor 70Yb and 82Pb are

shown in Figures 18 and 19, where f12 = .199 and .072 for

70Yb and Pb, respectively. Figures 18 and 19 are

102

103

representative of the rest of the target-ion systems. Thus

the term f1 2 aL1Ly is very small compared to aL2/Ly and

Eq. A-2 can be approximated by

K = 2 (A-3)Ly1

This indicates that aLy is dominated by aL2

Similarly, from Eq. IV-2, one can write

Ka = a + f a + (f f + f )a , (A-4)Lyl, 2 L3+23 L2+ 12 23 13 L,

where K = r3W3/ 3a + r 3 a2). Dividing Eq. A-4 by GLal,2yields

CL L YL

K = + f2+ 3+ f 13 . (A-5)Ly, 2 Ly,2 1 2 La1,2

The values of f23 are less than 0.152. From the

characteristics shown in Figures 18 and 19, it is obvious

that f23 aL2 /Lyl, 2 is small compared to aL3/La/L2 and can

thus be neglected. The factor (f1 2f2 3 + f1 3) is less than

.35 for all targets except 8 2Pb, where (f1 2f23 + f13) = .66.

However, from Figures 18 and 19 it can be observed that

aL1/aLa .,2is small compared to aL3 /Lal,2 and when

104

aL La,2is multiplied by the factor (f 2f23 + f13), whichL 1Lacz2 223 1

is less than 1, it becomes even smaller compared to aL3/aLal,2

Consequently, Eq. A-5 can be approximated by

cLK = -- 3 (A-6)

and thus it becomes clear that a Lal,2is dominated by aL3

105

CL2

20

Lyr

10

4PWBA Theory for 2He on 70Yb

5

4 aL 3Lai,2

3 L L 2a

2 G a 1'La 1V2

0.4 1.2 2.0 2.8 3.6 4.4

Energy (MeV/amu)

Figure 18

30 t

20

10

4

c-

- Ly1

4

PWBA Theory for 2 He on 8 2 Pb

L

cL

cL

cr L

34-

I2

I.

0.4

II I-I ---I-- ----I- - 9 -- --- -1I

1 .2.

2. 8.

2.0

Energy (MeV/amu)

Figure 19

106

50

40

# Lal

.3.6 4.4

*

-

-

*

ow do

a