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Determination of Multiply Scattered Gamma Ray Energy Spectra in Water by the Monte-Carlo Method
Remziye Ergül, Gökay Kaynak
To cite this version:
Remziye Ergül, Gökay Kaynak. Determination of Multiply Scattered Gamma Ray Energy Spectra in Water by the Monte-Carlo Method. Journal de Physique III, EDP Sciences, 1995, 5 (11), pp.1917- 1921. �10.1051/jp3:1995234�. �jpa-00249425�
Classification Physics Abstracts 25.20
Determination of Multiply Scattered Gamma Ray Energy
Spectra in Water by the Monte-Carlo Method
Remziye Ergfil and G0kay Kaynak
University of Uluda(, Faculty of Science and Art, Physics Department, 16059 Bursa, Turkey (Received 13 December 1995, revised 15 June 1995, accepted lo July 1995)
Abstract. The spectral distribution of multiply scattered gamma ray energy in water is determined by the Monte Carlo sampling technique in the energy range o-S -1.6 MeV. It is found that the energy for which the scattered photon number is
a maximum, is related to the
source energy and this is in agreement with studies made by Minato for a point source in different
media.
1. Introduction
As a result of increasing use of nuclear energy, the possibility of gamma active nuclei being
emitted into the atmosphere, soil and water through nuclear tests or possible accidents is also increased. The determination of gamma radiation scattered into the water is important for the well-being of mankind and for environmental reasons. The effect of gamma radiations on
humans and on the environment depends on their energy.
Nuclear tests and accidents can result in the emission of radio-isotopes into atmosphere and water, with gamma energies in the range of 30 kev to 1.6 MeV iii.
In this study, the source energy in the 0.5-1.6 MeV range is considered as a series of point
sources distributed uniformly in an infinite water medium as they would be in the case of a
nuclear accident or a nuclear explosion. This range is divided into 12 sectors each with a width of 0.1 MeV. The distribution of scattered gamma ray energy in water is determined by the
Monte Carlo sampling teclmique for these 12 separate energies.
In a melium,
gamma rays interact with atoms principally by three mechanisms. These are the photoelectric effect, the Compton scattering and pair production. In this study, the effect of pair production is neglected because the threshold energy is 1.022 MeV. Also, coherent
scattering and bremsstrahlung events are disregarded because their effects are negligible.
For the change of reaction cross-section with energy, previously developed continuous func- tions are used.
Q Les Editions de Physique 1995
1918 JOURNAL DE PHYSIQUE III N°10
E= 5 MeV E= 6
fl E
E#
c
c °
°
~
~
0
025 0 0 175 0 25 a 325 0 4 0 475 0 03 0 12 0 21 0 3 0 39 0 48 0 57
Energy [MeV) Energy (MeV]
E= 7 MeV E= 8 MeV
fl$ fl
#
c c
° °
I I
~ ~
0
0 035 0 14 0 245 0 35 0 455 0 56 0 665 0 04 0 16 0 28 0 4 0 52 0 64 a 76
Energy [MeV] Energy ]Mevj
E= 9 MeV E=1 0 MeV
fl fl
E E
C C
o o
3 3
f f
045 0 18 0 315 0 45 0 585 0 72 a 855 0 05 0 2 0 35 0 5 0 65 08 0 95
Energy lMeV] Ene,gy lMeV]
E=1 MeV E=1 2 MeV
) i
E I
~ C
~
[ C°
E I
~ ~
0
0 22 0 385 0 55 0 715 0 88 045 0 06 0 24 0 42 0 6 a 78 0 96 14
Energy jMeV] Energy (MeV]
Fig. 1. The variation of photon number with respect to energy.
E=1 3 MeV E=1 4 MeV
fl fl
E E
#
8 I
B 3
f f
065 0 26 0 455 0 65 0 845 04 1235 0 a7 0 28 0 49 07 0 91 12 33
Ene,gy imevl Ene,gy [MeV)
E=1 5 MeV E=1 6 MeV
~
~
c ~
fi
75
Energy
Fig. 1. (Continued).
2. Method
Gamma rays emitted in water at any instant from any point can cause photoelectric effects or Compton scattering with probabilities depending on their energies. To determine which effects happen, we must have a knowledge of the cross-sections at this energy.
However, there are no continuous functions available in the literature, that relate the cross- section to energy for the events considered. Researchers use batch values given in references [2,3] and try to find undefined reaction cross-sections by interpolation. This procedure requires
considerable computer time and gives only approximate results. In the present study, reaction cross-section values are found for various energies by using continuous functions derived by the authors. These functions result in values which are in good agreement with the values given
in reference [2].
The variation of the cross-sections with energy for the photoelectric effect and the Compton scattering are given below.
~f(E)
= exp( -22.403481 0.7422581E + 47.095972 exp(-1.6335308E°.~~~~~~~)) (1)
~~~~~
4.5838562 + 14.833619E +
.1053207E2
+ 1.8448183E3 ~~~
In these functions, ~ is in cm2/g and E is in MeV.
1920 JOURNAL DE PHYSIQUE III N°10
In this study, we first determine which event occurs because of a gamma ray. In the pho-
toelectric effect, a gamma ray transfers its whole energy to the medium. But in Compton scattering, the photon loses part of its energy and is scattered at an angle b in the direction of
incidence. The relationship between the incident photon and the scattered photon (where E is incident energy) is given by
~'
1 + ii ~cosb)k' ~~~
The energy E' of the scattered photon depends on the cosine of the scattering angle, for which the following equation is used [4].
CDS b
= flq, kill)]
= 2q 1 + lq q~)[al lk) + a21k)q + a3(k)q~ + a4(k)q~i 14) In this equation q indicates random numbers between 0 and 1 and ai(k), a2(k), a3(k), a4(k),
are coefficients given by:
ai(k)
= 5.6613((1.5233-exp(0.043334k))-3.5376exp(-0.39113k)
a2(k)
= 37.047(1 + 0.0011 739k) + 99.969
~ ~~~j(~~~~~~~~ ~~~~
a3(k)
= 40.238(1 + 0.0031476k) 104.51
~ ~ ~'~~~~~
~~ ~ ~~ ~
(~ ~ o ~~~)o.924
~ ~~~~~ ~ ~ ~~~~~
a4(k)
= 20.9+54.28
_
j
~
In the equations above, k
=
~
~.
The accuracy of this angular distribution has been tested moc
for the energy range up to k
= 40 [4]. Through this procedure the Compton scattered photon energy can be determined.
In this study, photons with 12 different energy intervals in the range 0.5-1.6 MeV have been examined until they interact by the photoelectric effect or their energy falls below 10 kev.
Each source energy is divided into 20 equal sequential energy bins. A photon loses its primary
energy after Compton scattering. The energy of the scattered photon is calculated and stored in the relevant energy bin. When a photon interacts by the photoelectric effect, a new photon
is generated and the same procedure is followed. Each spectrum is calculated for 10 000 photon histories.
3. Result and Discussion
The histograms in Figure 1 show the variation of scattered photon number with respect to energy for the 12 different source energies. Each spectrum represents multiple scattering events.
These curves indicate that there is a maximum scattered photon number which corresponds
to an energy range for each source energy. Figure 2 indicates that the energy range related to the maximum scattered photon number, changes linearly with source energy and consists of two regions. We found that the energy for which the photon number is a maximum is related
to the source energy by the following formulas:
Em = 0.1 E for 0.5 < E < 1.0 MeV
Em = 0.05 E for 1.0 < E < 1.6 MeV is)
I lim=0.I E
~ 0.
~
~
~
lim=0 05 E0.6 O.8 1.2 1.4 1.6 1.8
Source Energy (MeV)
Fig. 2. Variation of maximum photon energy with related
source energy.
In this respect, equation (5), which relates the energy at which the photon number is a maximum to the source energy, is quite remarkable. Minato has suggested that there may be a linear relationship between the maximum photon energy and the source energy for a
point source [5j. In this study, this relation is indeed obtained for uniformly distributed source energies.
Also, the use of continuous functions, instead of batch values taken from tables, is specific
to this study.
References
ill Nuclear Data Proj. Rept. ORNL- 5114 (1976).
[2j Hubbell J-H-, National Bureau of Standards, NSRDS- NBS 29 (1969).
[3j Storm E. and Isreal H-J-, Nucl. Data Tables A7 (1970) 565.
[4j Ozmutlu, E-N-, Sampling of Angular Distribution in Compton Scattering, Appi. Radial. Isot. 43
(1992) 713-715.
[5j Minato S., Calculation of the Energy Spectra of Reflected Gamma Radiation by Monte Carlo
Method, Reports of Government Industrial Research Institute, Nagoya, Vol. XXI, No. 7 (1972).
Commission paritaire N° 57920
© Les Editions de Physique 1995 Directrice de la Publication : Jeanne BERGER
SaisieT£X-LAT@X: Les Editions de Physique Impression JOUVE, 18, rue Saint-Denis, 75001 PARIS
N° 231176U. Dbpbt14gal Novembre 1995