appraisement of the correction factors for neutron reaction in the manganese bath using monte carlo...

Appraisement of the correction factors for neutron reactionin the manganese bath using Monte Carlo calculation

Rahim Khabaz

Received: 17 October 2011 / Published online: 26 April 2012

� Akademiai Kiado, Budapest, Hungary 2012

Abstract In this work, the Monte Carlo method has been

used to simulate the manganese sulfate bath calibration

system, in order to evaluate the different interaction of

neutron with all nuclei of the components of the solution,

i.e., hydrogen, manganese, sulfur, and oxygen nuclei for241Am–Be and 252Cf neutron sources. Also, the leakage

probability of neutron has been calculated for various

radiuses of spherical bath containing a solution with weight

concentration of 93.68 g/(kg of solution). The simulations

performed by MCNPX, included a detailed description of

the geometry and material of the system (tank, holder and

source). The calculations were evaluated using neutron

cross sections from several libraries. The results of calcu-

lation show that the proper radiuses of spherical manganese

bath with this concentration, for 252Cf and 241Am–Be

sources, are about 35 and 60–65 cm, respectively.

Keywords Manganese bath � Neutron source � Correction

factor � Monte Carlo method

Introduction

In recent years, using the radio-isotopic neutron sources

have increased, so having knowledge such as their neutron

emission rate and energy spectrum are essential [1, 2]. The

manganese sulfate (MnSO4) bath technique is a widely

used method for the absolute determination of the neutron

emission rate of radio-isotopic neutron sources [3]. The

method consists of activating a solution of manganese

sulfate with a neutron source placed at the center of a

relatively large aqueous solution and inferring the strength

of the neutron source (Q) from the manganese activity of

the bath, by the 55Mn (n,c)56Mn reaction which has a half-

life of 2.5785 h [4].

The main capture reactions of fast neutrons are the type

(n,a), (n,d) and (n,p). In the solution of manganese sulfate,

the nuclei of the 16O and 32S often capture fast neutrons

through 16O(n,a)13C, 32S(n,a)29Si and 32S(n,p)32P reactions

and the other reactions is negligible compared to these [5].

The neutrons emitted from the source will be slowed

down, particularly through elastic scattering with hydrogen

nuclei. The created thermal neutrons are captured by the

nucleus produce reactions of type (n,c), which are likely to

occur for nearly all chemical elements (55Mn, 1H, 16O and32S). The thermal neutron-capture cross-section of oxygen

nuclei is negligibly small compared to those of the other

nuclei [5]. Neutron capture by hydrogen produces a stable

nucleus, a deuteron, and neutron capture by sulfur produces

a stable isotope, 33S. A fraction of the neutrons is absorbed

in manganese by (n,c) corresponds to the number of neu-

trons emitted from the neutron source. The c-rays of 56Mn

are counted with a NaI(Tl) scintillation detector at a well

shielded location by continuously pumping a fraction of the

MnSO4 solution to it.

For that activity to give the value of Q is necessary to

accomplish some types of corrections. The source strength,

Q, of the neutron source is obtained from the following

well known equation [6]:

Q ¼ RMn �1

f� 1e� 1

1� Ceð Þ 1� Csð Þ 1� Ccð Þ ð1Þ

where RMn—saturation count rate of the 56Mn measured by

the bath detector system, e—counting efficiency in NaI(Tl)

R. Khabaz (&)

Physics Department, Faculty of Sciences, Golestan University,

49138-15739 Gorgan, Iran

e-mail: [email protected]; [email protected]

123

J Radioanal Nucl Chem (2012) 293:455–462

DOI 10.1007/s10967-012-1792-0

detector which was fixed using 4pb–c coincidence

counting method [7], Ce—fractional neutron escape from

the boundaries of the bath, Cs—fraction of neutron

recaptured by the source and its mounting assembly,

Cc—fraction of neutron captured in the (n,p) and (n,a)

reactions by the nuclei of the components of the solution,

i.e., manganese, sulfur, and oxygen nuclei, f—fraction of

the remaining neutron captured by manganese in absence

of impurities in 55Mn(n,c)56Mn reaction:

1

f¼ 1þ rS

rMnð1þ G�rsÞMn

þ 4rO

rMnð1þ G�rsÞMn

þ NH

NMn

� rH þ 0:5rO

rMn 1þ G�rsð ÞMn

ð2Þ

where NMn, NH—concentrations of manganese and

hydrogen nuclei per cubic centimeter in the MnSO4 solu-

tion, rMn, rS, rH, rO—thermal neutron capture cross sec-

tions of manganese, sulfur, hydrogen and oxygen,

respectively.

The factor ð1þ G�rsÞ allows for the resonance capture in

manganese [8]. Indeed, in Eq. (2) the resonance capture

cross-section at the epithermal region for manganese nuclei

has been corrected by replacing the thermal neutron-cap-

ture cross-section rMn, with rMnð1þ G�rsÞ [9], where G is

the resonance self-shielding factor for the solution, �r: is a

spectral index averaged over the system and represents the

relative amount of the non-Maxwellian component of the

neutron energy distribution, and s is the resonance activa-

tion integral normalized to the thermal neutron-capture

cross section.

As discussed one method to determination of correction

factors for manganese sulfate bath is analytical solving the

Eqs. (1) and (2). By utilize the proper cross section of

different reaction for neutrons with various energies, the

correction factors can be given as a function of energy.

Because of the complication and using the approximation,

this process is not simple and accurate. As well as, the loss

regarding capture for the material of the source and

immersion system (Cs) cannot fix experimentally. Nowa-

days, with developed neutron transport and to the well-

evaluated nuclear cross-sections, individual evaluations of

the various correction factors can be abandoned and

replaced by a direct calculation of the probability of the

neutron capture by manganese nuclei, by using the Monte

Carlo method. The probability, PMn, of neutron absorption

by manganese nuclei in the actual bath with the actual

source can be directly calculated using an appropriate

Monte Carlo neutron transport code, e.g., MCNPX. Fur-

thermore, in this way, it is possible to consider quite easily

the energy spectrum of the source and the influence of all

construction materials. The source emission rate (Q) is then

given by the calculated probability PMn and the production

rate (RMn) of 56Mn by neutron capture,

Q ¼ 1

e� 1

PMn

� RMn ð3Þ

where by comparison between Eqs. (1) and (3) gives

1

PMn

¼ 1

f� 1

1� Ceð Þ 1� Csð Þ 1� Ccð Þ ð4Þ

In this work, the correction factors for neutron losses with

different process in all nuclei of solution are given for two

well-known sources, namely 241Am–Be and 252Cf by

Monte Carlo simulation included a detailed description of

the geometry and material using the MCNPX code. The

calculation was performed for various radiuses of spherical

bath, and suitable radius was determined for calibration of

each source. Consequently, one can acquire the neutron

rate of emission rate of the neutron source by experimental

measurement of the gamma emission rate of 56Mn in the

NaI(Tl) detector and using the calculated correction

factors.

Materials and methods

In this work the MCNPX Monte Carlo code with the

ENDF/B-VI.0, ENDF/B-V, ENDF/BVI.8 and ENDF/B-

VII.0 libraries was employed to calculate the correction

factors [10].

The geometry and the material composition of the bath

and the neutron source container were precisely described

in the MCNPX input file. The simulation was performed

for 241Am–Be and 252Cf neutron sources that their spec-

trum was extracted from the standard ISO 8529-1 [11]. The241Am–Be source was defined as a cylinder of beryllium

(with a density of 1.85 g/cm3) contained in a X.14 type

capsule with 60 mm in height and 30 mm in diameter. The

geometry 252Cf neutron source was modeled as a cylinder

of californium oxide (with a density of 15.10 g/cm3) filled

in a X.224 type capsule by dimensions of 32.5 mm in

length and 9.4 mm in outer diameter. The container cap-

sules of 241Am–Be and 252Cf sources constructed of 1.6

and 2.4 mm thickness of stainless steel (316L. type),

respectively.

The source was placed in a cylindrical Teflon (CnF2n?2)

holder (by density of 2.20 g/cm3) with 10 cm in height,

10 cm in diameter and 4.0 mm thickness. The inner space

of the Teflon container was assumed to be the air (with

density of 1.29 kg/m3 with elemental composition of

79.1 % N and 20.9 % O). This holder also was installed in

the center of a spherical tank which was had been filled

with an aqueous solution of pure MnSO4 (Fig. 1). The

container bath consisted of 3.0 mm thickness of stainless

steel (316L. type) with density of 7.93 g/cm3 whose ele-

mental composition was 1.000 % Si, 0.045 % P, 0.030 %

456 R. Khabaz

123

S, 0.030 % C, 17.000 % Cr, 65.395 % Fe, 12.000 % Ni,

2.000 % Mn and 2.5.000 % Mo (in terms of their weight

percentage in the composition) [12].

The set of bath used in this study consists of eight

stainless steel spherical tanks filled with manganese sulfate

solution. The weight concentration of MnSO4 in the solu-

tion was considered 93.68 g/(kg of Solution), and the

solution density was 1.0934 g/cm3 [13]. There are some of

the characteristics of the manganese baths simulated by

MCNPX in Table 1.

The number of each nuclear component of the solution

is deduced from the present concentration and density. The

concentrations of nuclei of the solution in units of nuclei/

barn-cm were 4.085 9 10-4 for manganese and sulfur, also

3.475 9 10-2 and 6.624 9 10-2 for oxygen and hydrogen,

respectively. Then the number ratio of hydrogen nuclei to

manganese nuclei was 162.15. The unusual ratio was

determined by the amount of high purity MnSO4 available

for the experiment. This ratio will be decreased as the

concentration increases.

Furthermore, it has been determined that the gamma

counting rate of the NaI(Tl) detector is increased with

decreasing the concentration of the solution [14]. This is

due to decreasing self-absorption of the 56Mn radiation as

the content of the solution decreases.

The calculation of the neutron capture for the solution,

source and immersion system was accomplished being

selected the tally F4 of MCNPX, being considered the

different reactions, associated to a card multiplier that

contains the volume of the solution, and the atom density

(atom/barn-cm) of the element (from Table 1) that interacts

for capture of neutrons. In the case of the leakage of

neutrons of the bath, this was estimated with the tally F1.

This tally was defined in a concentric external spherical

surface of the tank, and it represents the number of parti-

cles that cross the surface in any direction.

Result and discussion

Different reactions were calculated using Monte Carlo

MCNPX code for described geometry, material and sour-

ces. Indeed, (n,c), (n,p) and (n,a) reactions were evaluated

in all nuclei of MnSO4�H2O. The results of these calcula-

tions by using ENDF/B-VI.0 for the 241Am–Be and 252Cf

sources were given in Tables 2, 3, 4 and 5. It should be

noted that the calculations are normalized to one neutron of

source. The relative error (D) for each tally is listed in these

tables. The statistical errors in output of MCNPX for all

reactions, except 16O(n,p)16N, by the 241Am–Be and 252Cf

sources were less than 0.4 and 1 %, respectively. Also, for

recorded (n,p) reaction in 16O that has least probability and

very small amounts, relative error was under 6 %.

As it can be observed, for two sources in all radiuses the1H(n,c)2d reaction has a maximum probability compared to

other reactions. Considering the important role of the ratio

of NH/NMn in the solution, and the conditions of mea-

surement, the appropriate concentration of manganese

sulfate should be used. For oxygen nuclei, the dominant

reaction is (n,a), while this element has an insignificant

amount of thermal neutron capture by (n,c). In reaction of

fast neutrons with sulfur nuclei, (n,p) is dominant, as for241Am–Be source the ratio of S(n,p) to S(n,a) is about 1.90,

while for 252Cf source, this ratio is less and about 1.05. The

interaction of thermal neutrons with sulfur through32S(n,c)33S has the most contribution among the other

neutron interactions.

The most important reaction in calibration of neutron

source by manganese bath is 55Mn(n,c)56Mn. The proba-

bility of this reaction in different baths for 241Am–Be and

Fig. 1 Geometry of manganese bath in Monte Carlo simulation

Table 1 Some parameters of various manganese sulfate baths in

calculations

Tank no. Radius (cm) Volume (l) Mass of MnSO4 (kg)

1 35 1.787 9 102 18.173

2 40 2.672 9 102 27.171

3 45 3.808 9 102 38.724

4 50 5.227 9 102 53.153

5 55 6.960 9 102 70.776

6 60 9.039 9 102 91.914

7 65 1.149 9 103 116.884

8 70 1.436 9 103 146.008

Appraisement of the correction factors 457

123

252Cf source increases from 1.594 to 1.885 and 1.887 to

1.973 with increasing the radius, respectively. Although

other reactions such as (n,p) and (n,a) occur in manganese

nuclei, the probability of these reactions is negligible in

comparison to the (n,c) reaction. As well as, the correction

factors in Eqs. (1) and (2) were calculated for all

Table 2 Result of the MCNPX calculation by using ENDF/B-VI.0 for various radiuses of manganese bath (35, 40, 45 and 50 cm) with the241Am–Be source

Reaction r = 35 cm r = 40 cm r = 45 cm r = 50 cm

Probability D (%) Probability D (%) Probability D (%) Probability D (%)

H (n,c) 6.35E-01 0.09 6.81E-01 0.08 7.08E-01 0.07 7.28E-01 0.06

O (n,c) 1.91E-04 0.09 2.05E-04 0.08 2.13E-04 0.07 2.19E-04 0.06

O (n,p) 4.09E-06 3.10 4.20E-06 3.19 4.26E-06 3.24 4.22E-06 2.85

O (n,a) 3.87E-02 0.20 3.97E-02 0.20 4.02E-02 0.21 4.07E-02 0.18

S (n,c) 6.00E-03 0.09 6.44E-03 0.08 6.69E-03 0.07 6.87E-03 0.06

S (n,p) 1.35E-03 0.13 1.39E-03 0.14 1.41E-03 0.14 1.42E-03 0.13

S (n,a) 7.09E-04 0.10 7.31E-04 0.11 7.43E-04 0.11 7.53E-04 0.10

Mn (n,p) 3.30E-05 0.22 3.38E-05 0.23 3.42E-05 0.23 3.46E-05 0.21

Mn (n,a) 1.15E-05 0.31 1.17E-05 0.32 1.19E-05 0.33 1.20E-05 0.29

Cc 4.08E-02 3.13 4.19E-02 3.23 4.24E-02 3.28 4.29E-02 2.88

(1 - Cc)-1 1.04 0.13 1.04 0.14 1.04 0.15 1.05 0.13

Mn (n,c) 1.59E-01 0.09 1.71E-01 0.08 1.78E-01 0.07 1.83E-01 0.06

1/PMn 6.27 0.09 5.85 0.08 5.63 0.07 5.47 0.06

Leakage 1.52E-01 0.31 9.35E-02 0.40 5.72E-02 0.53 3.46E-02 0.6

(1 - Ce)-1 1.18 0.06 1.10 0.04 1.06 0.03 1.04 0.02

Source absorption 7.52E-03 4.13 7.65E-03 3.86 7.93E-03 3.81 8.05E-03 3.24

(1 - Cs)-1 1.01 0.03 1.01 0.03 1.01 0.03 1.01 0.03

The symbols are defined in the text

Table 3 Result of the MCNPX calculation by using ENDF/B-VI.0 for various radiuses of manganese bath (55, 60, 65 and 70 cm) with the241Am–Be source



H (n,c) 7.38E-01 0.05 7.45E-01 0.05 7.49E-01 0.05 7.51E-01 0.05

O (n,c) 2.22E-04 0.05 2.24E-04 0.05 2.25E-04 0.05 2.26E-04 0.05

O (n,p) 4.17E-06 2.29 4.19E-06 2.31 4.20E-06 2.33 4.21E-06 2.33

O (n,a) 4.09E-02 0.15 4.10E-02 0.15 4.11E-02 0.15 4.12E-02 0.15

S (n,c) 6.97E-03 0.05 7.03E-03 0.05 7.07E-03 0.05 7.09E-03 0.05

S (n,p) 1.43E-03 0.11 1.44E-03 0.11 1.44E-03 0.11 1.44E-03 0.11

S (n,a) 7.58E-04 0.08 7.61E-04 0.08 7.63E-04 0.08 7.64E-04 0.08

Mn (n,p) 3.48E-05 0.17 3.49E-05 0.17 3.50E-05 0.17 3.50E-05 0.17

Mn (n,a) 1.21E-05 0.24 1.21E-05 0.24 1.21E-05 0.24 1.21E-05 0.24

Cc 4.31E-02 2.32 4.33E-02 2.34 4.34E-02 2.36 4.34E-02 2.36

(1 - Cc)-1 1.05 0.11 1.05 0.11 1.05 0.11 1.05 0.11

Mn (n,c) 1.85E-01 0.05 1.87E-01 0.05 1.88E-01 0.05 1.88E-01 0.05

1/PMn 5.40 0.05 5.35 0.05 5.32 0.05 5.31 0.05

Leakage 2.09E-02 0.62 1.25E-02 0.81 7.51E-03 1.05 4.52E-03 1.34

(1 - Ce)-1 1.02 0.01 1.01 0.01 1.01 0.01 1.00 0.01


(1 - Cs)-1 1.01 0.03 1.01 0.03 1.01 0.03 1.01 0.03


458 R. Khabaz

123

geometries. As it can be seen, the minimum deviation of

these from the ideal condition (i.e., if all neutrons are

thermalized and captured by the 55Mn nuclei) is for the

factor of neutron recaptured by the source and its mounting

assembly. By the both sources, the factor of leakage from

the bath boundaries has the maximum deviation for spheres

Table 4 Result of the MCNPX calculation by using ENDF/B-VI.0 for various radiuses of manganese bath (35, 40, 45 and 50 cm) with the 252Cf

source



H (n,c) 7.52E-01 0.07 7.69E-01 0.07 7.76E-01 0.06 7.82E-01 0.06

O (n,c) 2.26E-04 0.07 2.31E-04 0.07 2.33E-04 0.06 2.35E-04 0.06

O (n,p) 1.80E-05 5.59 1.87E-05 5.69 1.90E-05 5.78 1.94E-05 5.86

O (n,a) 5.66E-03 0.55 5.77E-03 0.56 5.82E-03 0.56 5.88E-03 0.57

S (n,c) 7.10E-03 0.07 7.26E-03 0.06 7.33E-03 0.06 7.38E-03 0.06

S (n,p) 3.14E-04 0.31 3.19E-04 0.32 3.21E-04 0.32 3.24E-04 0.33

S (n,a) 3.02E-04 0.18 3.06E-04 0.19 3.08E-04 0.19 3.10E-04 0.19

Mn (n,p) 3.60E-06 0.72 3.68E-06 0.74 3.73E-06 0.76 3.77E-06 0.77

Mn (n,a) 9.22E-07 0.99 9.47E-07 0.98 9.59E-07 0.95 9.71E-07 0.94

Cc 6.30E-03 5.76 6.42E-03 5.86 6.48E-03 5.94 6.53E-03 6.02

(1 - Cc)-1 1.01 0.04 1.01 0.04 1.01 0.04 1.01 0.04

Mn (n,c) 1.89E-01 0.07 1.93E-01 0.07 1.95E-01 0.06 1.96E-01 0.06

1/PMn 5.30 0.07 5.18 0.07 5.13 0.06 5.09 0.06

Leakage 4.61E-02 0.58 2.35E-02 0.82 1.22E-02 1.15 6.49E-03 1.59

(1 - Ce)-1 1.00 0.03 1.02 0.02 1.01 0.01 1.01 0.01


(1 - Cs)-1 1.00 0.01 1.00 0.01 1.01 0.01 1.00 0.01


Table 5 Result of the MCNPX calculation by using ENDF/B-VI.0 for various radiuses of manganese bath (55, 60, 65 and 70 cm) with the 252Cf

source



H (n,c) 7.84E-01 0.05 7.85E-01 0.04 7.86E-01 0.04 7.86E-01 0.04

O (n,c) 2.36E-04 0.05 2.36E-04 0.04 2.36E-04 0.04 2.36E-04 0.04

O (n,p) 1.89E-05 4.19 1.90E-05 4.22 1.91E-05 4.25 1.92E-05 4.27

O (n,a) 5.91E-03 0.41 5.92E-03 0.41 5.93E-03 0.41 5.93E-03 0.41

S (n,c) 7.40E-03 0.04 7.41E-03 0.04 7.42E-03 0.04 7.42E-03 0.04

S (n,p) 3.24E-04 0.23 3.25E-04 0.23 3.25E-04 0.23 3.25E-04 0.23

S (n,a) 3.10E-04 0.14 3.11E-04 0.14 3.11E-04 0.14 3.11E-04 0.14

Mn (n,p) 3.78E-06 0.55 3.79E-06 0.55 3.80E-06 0.55 3.80E-06 0.56

Mn (n,a) 9.76E-07 0.94 9.80E-07 0.93 9.83E-07 0.92 9.84E-07 0.93

Cc 6.57E-03 4.36 6.58E-03 4.38 6.59E-03 4.41 6.60E-03 4.43

(1 - Cc)-1 1.01 0.03 1.01 0.03 1.01 0.03 1.01 0.03

Mn (n,c) 1.97E-01 0.04 1.97E-01 0.04 1.97E-01 0.04 1.97E-01 0.04

1/PMn 5.08 0.04 5.07 0.04 5.07 0.04 5.07 0.04

Leakage 3.47E-03 1.53 1.93E-03 2.07 1.07E-03 2.78 6.00E-04 3.69

(1 - Ce)-1 1.00 0.01 1.00 0.004 1.00 0.003 1.00 0.002


(1 - Cs)-1 1.00 0.01 1.00 0.01 1.00 0.01 1.00 0.01



123

with radiuses up to 45 cm, and for larger radiuses the fast

neutron reaction has the maximum effect.

Moreover, for the evaluation of correction factors, the

MCNPX code was used together with the neutron cross

section from other libraries, such as ENDF/B-V, ENDF/B-

VI.8 and ENDF/B-VII.0. For both types of neutron sources,

the variations of all probabilities calculated with all dif-

ferent libraries, except 16O(n,a)13C, were negligible.

The probability of 16O(n,a)13C has the main loss by the

fast neutron reactions in the bath. Therefore, the only cross

section which will introduce an appreciable error in the

correction factors is the 16O(n,a). A comparison of the16O(n,a)13C capture fraction calculated using different

libraries for the various baths with the two sources are in

Table 6. It can be observed that there is a little reduction

when using ENDF/B-VI.8 instead of ENDF/B-VI.0, and a

much greater reduction when using ENDF/B-VII.0.

Figures 2 and 3 show the probability of the total capture

reactions in oxygen and sulfur as a function of bath radius

for 241Am–Be and 252Cf source, respectively. It may be

observed that the probability of these reactions increase

with radius. Also, because of difference between energy

spectrum of two sources, for 241Am–Be the oxygen in

comparison to sulfur has a greater role in capturing the

neutron, and for 252Cf source is inverse, i.e., neutron cap-

ture of sulfur is more. This effect is because of the fission

source spectrum is fairly soft compared to the (a,n) source

spectrum and also total cross section (without elastic

scattering) of sulfur in low energy is higher than total cross

section of oxygen [5].

The probability of 1H(n,c)2d reaction as a function of

bath radius is shown in Fig. 4. As it can be seen, for 252Cf

source the rate of this reaction is more, especially for

smaller baths (This is due to 1/v form of cross section for

this reaction). The deuteron nuclei are stable and produced

gamma from it will be stopped with removing of the source

from the tank, and do not interfere in the spectrum of

gamma measured in NaI(Tl) detector. However, it should

be noted that in the long time, created deuterons will be

acted as impurities in the solution.

Figure 5 shows the probability of total capturing reac-

tions in manganese as a function of bath radius for 241Am–

Be and 252Cf source; however, the (n,c) reaction has a main

contribution of neutron capture in this nucleus. It can be

Table 6 Oxygen (n,a) capture fraction for 241Am–Be and 252Cf sources using several cross section libraries

r (cm) ENDF/B-VI.0 ENDF/B-VII.0 ENDF/B-VI.8 ENDF/B-V

241Am–Be 252Cf 241Am–Be 252Cf 241Am–Be 252Cf 241Am–Be 252Cf

35 3.87E-02 5.66E-03 2.72E-02 4.69E-03 3.41E-02 5.34E-03 2.83E-02 5.13E-03

40 3.97E-02 5.77E-03 2.75E-02 4.77E-03 3.54E-02 5.44E-03 2.96E-02 5.26E-03

45 4.02E-02 5.82E-03 2.81E-02 4.84E-03 3.63E-02 5.55E-03 2.99E-02 5.31E-03

50 4.07E-02 5.88E-03 2.85E-02 4.87E-03 3.66E-02 5.63E-03 3.01E-02 5.36E-03

55 4.09E-02 5.91E-03 2.87E-02 4.90E-03 3.68E-02 5.68E-03 3.02E-02 5.38E-03

60 4.10E-02 5.92E-03 2.87E-02 4.92E-03 3.70E-02 5.69E-03 3.03E-02 5.39E-03

65 4.11E-02 5.93E-03 2.88E-02 4.92E-03 3.70E-02 5.69E-03 3.04E-02 5.40E-03

70 4.12E-02 5.93E-03 2.88E-02 4.93E-03 3.71E-02 5.70E-03 3.05E-02 5.40E-03

Fig. 2 Total probability of interaction of neutrons with 16O and 32S

for 241Am–Be source by using ENDF/B-VI.0

Fig. 3 Total probability of interaction of neutrons with 16O and 32S

for 252Cf source by using ENDF/B-VI.0

460 R. Khabaz

123

observed that for 252Cf source, with a mean energy about

2.2 MeV, the variations of 55Mn(n,c)56Mn with radius are

less than the variations of this reaction for 241Am–Be

source, with a mean energy around 4.5 MeV [15]. So, for

calibration of radio-isotopic neutron sources with low

mean energy can be used the smaller baths. As with this

concentration of manganese sulfate, a spherical tank with

about 35 cm diameter is usable for calibration of 252Cf

source.

Figure 6 shows the probability of escape from the

boundary of bath as a function of tank radius for both

sources. For both types of neutron sources, the statistical

uncertainty of the leakage probabilities calculated with four

different libraries, i.e., ENDF/B-VI.0, ENDF/B-V, ENDF/

B-VI.8 and ENDF/B-VII.0, was 0.18 % or less.

As it can be seen, the leakage of neutron is decreased

with radius. If the leakage from the bath must be less than

about 1 % [16, 17], then for having a suitable efficiency in

calibration of 241Am–Be source (according to Fig. 5 the

slope of radius larger than 60 cm is negligible), the radius

of tank with this concentration can be about 60–65 cm.

During this work, it was observed that the probability of

leakage (Ce) could be well fitted as a function of sphere

radius by the following exponential equation

Ce ¼ Co: exp � r � ro

t

� �ð5Þ

where r is the bath radius (cm) and Co, ro and t are

parameters that for two sources, based on results calculated

with ENDF/B-VI.0, are listed in Table 7.

Conclusions

The correction factors of some manganese bath system for

various radiuses have been calculated using a recent cross

section library by Monte Carlo MCNPX code. In the

simulations it was assumed that 241Am–Be and 252Cf

sources with different energy spectrum (mean energy of

about 4.5 and 2.2 MeV) have been located in the center of

manganese tank. Various objects affecting the manganese

activity of the bath have been calculated and studied, such

as (n,c), (n,p) and (n,a) reaction in the nuclei of the com-

ponents of the solution, neutron recaptured by the source

and its mounting assembly, and neutron leakage from the

boundaries of the bath. Although the calculation has been

Fig. 4 The probability of 1H(n,c)2d reaction as a function of bath

radius for two sources by using ENDF/B-VI.0

Fig. 5 The probability of 55Mn(n,c)56Mn reaction as a function of

bath radius for two sources using ENDF/B-VI.0

Fig. 6 The probability of leakage from the bath as a function of tank

radius for two sources calculated with different libraries

Table 7 Fitting parameters of Eq. (5) for the calculated leakage Ce

versus bath radius r with ENDF/B-VI.0

Source Co ro t

241Am–Be 0.1526 ± 0.0003 35.0 10.12 ± 0.04252Cf 0.0460 ± 0.0002 35.0 7.59 ± 0.06


123

performed only for one concentration of MnSO4 in the

solution [93.68 g/(kg of Solution)], the simulation can be

generalized for other concentrations. Maximum probability

of neutron capture was for hydrogen nuclei that the result is

the production of deuteron impurity; therefore, the ratio of

NH/NMn in manganese solution is the one of important

parameters.

The difference of the probability of all events, except16O(n,a), calculated by considering of various libraries was

insignificant; however, determination of the 16O(n,a)13C

reaction probability is one of the important challenges in

the manganese bath. It was observed that there is a slight

reduction when using ENDF/B-VI.8 instead of ENDF/B-

VI.0, and a much greater reduction when using ENDF/B-

VII.0; however, the results calculated using ENDF/B-V

and ENDF/B-VII.0 were approximately agreement. For252Cf source in compared to 241Am–Be, the differences

were less.

Also, the calculations described in this report have

shown that with this concentration, for calibration of 252Cf

and 241Am–Be source the spherical bath by 35 and

60–65 cm radius is proper, respectively.

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