Computation of neutron dose distribution in a cylindrical phantom of tissue equivalent materials

Annals of Nuclear Energy 26 (1999) 543±551

Technical Note

Computation of neutron dose distribution in a cylindrical phantom of tissue equivalent materials M.A. El-Kolaly a, S.H. Abdel Samie b, O.H. Sallam a,* a

ReactorandNeutron PhysicsDepartment,RadiationProtectionDepartment,NuclearResearchCentre,Atomic Energy Authority, Cairo, Egypt b El-Minia University, Faculty of Science, El-Minia, Egypt Received 9 March 1998

Abstract This work gives the total dose and the spectral distribution at any speci®c point inside a tissue equivalent cylindrical phantom due to Pu±Be neutron source. The absorbed dose through the material are coming from 17 reactions between the neutrons and the phantom constituents: H2,02,N2. and C. The changes in the neutron spectra are due to energy loss as a result of neutron slowing down. A computer program is used to carry out these calculations using the MonteCarlo technique. # 1999 Published by Elsevier Science Ltd. All rights reserved.

1. Introduction With increasing utilization of neutron sources as a nuclear facility, the computation of neutron dose within tissue equivalent materials is posing one of the biggest problems. This may be due to complex spectra of the neutron source as well as it is dicult to use exact shape and size of an organ for dose calculation under di€erent conditions. In case of tissue irradiated by fast neutrons the ranges of penetration distance of the heavy secondary charged particles (mainly protons) are short, relative to the mean free path `f ' of the neutrons. One can know the energy distribution of the neutrons incident at a point of interest in the tissue, when the primary neutron ¯ux incident upon the tissue sample as a whole is known. To calculate the absorbed dose, it is necessary to multiply the value of the dose from each type of atoms by the fractional composition (by weight ) of that type and sum the contribution of all *Corresponding author. 0306-4549/99/$ÐSee front matter # 1999 Published by Elsevier Science Ltd. All rights reserved PII: S030 6-4549(98)0003 8-3

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types of atoms. For a considered medium, when the size is comparable with the mean free path of neutrons in the medium, multiple collision calculations must be made to ®nd out the distribution of absorbed dose in the medium. Such calculations have been carried out for a tissue slab (Synder et al., 1957), which is 30 cm thick in the direction of a collimated broad beam of neutrons. Neutron dose and neutron spectrum have been computed by (Mottef et al., 1963). The measurement of the radiation transport through slabs of various shielding materials was performed in water media. However, neutron dose distribution in an in®nite slab of a standard mail composition have been determined using MonteCarlo calculation (Nagrajan 1968; Cramer et al., 1985) where neutron energies were ranging from thermal up to 10 Mev. In the present calculations it is intended to determine the dose distribution in the skull (head). This organ has been represented by a cylindrical phantom of standard man composition. It is 20 cm height and 20 cm diameter. A plutonium±beryllium (Pu±Be) neutron source of activity equal to 5 curies has been used for these calculations. A developed Monte-Carlo program is applied (Hurst, 1954; Iaslli, 1986). 1.1. Theory of calculations In this work, a short description is given for the Monte-Carlo technique developed for the computation of the neutron dose distribution in a right circular cylindrical phantom (Hurst, 1954; Iaslli, 1986). Fig. 1 gives the source phantom geometry. The source is located at S outside the cylinder. The cylinder is 20 cm in both diameter and height. The number of radial, angular and axial meshes to which the cylinder is divided are considered as 575, respectively, as shown in Fig. 1. The neutron at any time is fully de®ned by the following quantities: 1. the point r~i …xi ; yi ; zi † is the point of entry on the surface of the cylinder from the sources; 2. Ei …MeV† is the energy of the neutron after the collision at r~i ; 3. the weight Wi is a number which remains =1 unaltered until the ®rst event takes place at r~i , and ~ i …i ; i †. 4. the direction

~ o it su€ers collision at location r~1 as a result of which As the neutron moved along

~ its direction changes to 1 , energy to E1 and weight reduces to W1 . The di€erence (Wo ÿ W1 ) is the lost captured at r~1 . Thus the state of the neutron changes from So to S1 . In this way the state goes on changing to S2 ; . . . Sn ,where r~n is the ®rst location outside the cylinder. At each location r~i an energy deposition of (Eiÿ1 ! Ei ) MeV takes place. This tallies in the volume element containing r~i . Such tallies are done for a large number of independent histories or tracks In the phantom each starting with So and ending with Sn . The mean of the energy deposition in any volume element divided by its mass and multiplied by the conversion factor 1.610ÿ8 yields the mean dose In rad in this ~ o as given by a volume element. In principle an isotopic direction can be chosen for

o and o such as:

M.A. El-Kolaly et al./Annals of Nuclear Energy 26 (1999) 543±551

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Fig. 1. Sketch diagram for the cylindrical phantom.

Cos o ˆ Cos ‡ ‰1 ÿ CosŠR1

…1†

o ˆ 2R2

…2†

where  Is the angle shown in Fig. 2, R1 and R2 are random numbers drawn from a pseudo-random sequence which has a uniform distribution in the interval (0,1). To correct for the sampling bias in Eq. (1) the results are multiplied by a factor fc which is given by: fc ˆ 2…1 ÿ cos o †=4; 1 fc ˆ …1 ÿ cos o † 2

…3†

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M.A. El-Kolaly et al./Annals of Nuclear Energy 26 (1999) 543±551

Fig. 2. Illustrated sectional diagram in the cylinder to represent neutron penetration.

where the numerator is the solid angle made by the cone which just cover the whole phantom and the denominator is the total solid angle. A given neutron travels a certain distance, su€ers a scattering or capture event and in the case of the former changes the direction and energy and the process goes on until it leaks or captures. The distance S is the travelled distance between two successive collisions. It is distributed due to the density function as follows: f…S† ˆ t exp…ÿt S†

…4†

A random value S1 for this distance is chosen as S1 ˆ ÿ‰ln R3 Št …E†

…5†

where R3 is a random number like R1 and R2 and t is the total macroscopic neutron cross-section at energy E in the phantom material which is given by: t ˆ

X

i …E†

i …E† is the macroscopic cross-sections:

…6†

For the considered tissue materials in the phantom, where the consistuents are H2,C,N2 and O2, there are 17 scattering events. The energy range (from thermal to 14 MeV) is divided into 100 groups. At any given energy Ej , (where j is one of the 17 scattering reactions) the distance is given by S1 ˆ ÿ‰ln R3 Š=tj

…7†

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where Ej lies in the jth energy group, and the location r~1 is obtained as: ~ r~1 ˆ r~o ‡ S1

…8†

In the case of ®rst scattering W is represented by: Wnew ˆ Wold :Pscatj

…9†

where Pscatj ˆ scatj =tj

…10†

Pscatj is calculated and stored. In this method all event are treated as scattering collisions. Table 1 gives the serial number j and the ith type of scattering. The type of collision is randomly sampled as in Eq. (10), since P17 ˆ 1. Thus, the j-value randomly sampled decides the type of collision from among the 17 types given in Table 1. So, we have passed on from So to S1 . In the same way we pass on to S2 ; S3 ; S4 and so on. At the site r~1 , an energy deposition of Wo …Eo ÿ E1 † takes place. 2. Results and discussions At various sites energy depositions take place due to the particular type of collision. In the present work energy deposition due to recoil protons (type of reaction 1 Table 1 Serial no. j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Type i of scattering Elastic scattering with Elastic scattering with Elastic scattering with Elastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with Inelastic scattering with

H O O N O O O O C C N N N N N N N

1st level 2nd level 3rd level 4th level 1st level 2nd level 1st level 2nd level 3rd level 4th level 5th level 6th level 7th level

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in Table 1) is separately tallied for obtaining the proton recoil dose component. All energy depositions due to elastic heavy recoils (types of reactions 2, 3, 4 and 5 in Table 1) are tallied together for obtaining the heavy recoil dose component. Inelastic energy depositions are not tallied as they tend to be negligible. For actual tallying purposes, the space mesh volume within which a given r~i is located is found out and in that volume the tally is made. For this purpose, as mentioned earlier, the cylindrical phantom is divided into (575) or 175 elemental volumes. Any given r~i falls within any one of these 175 space blocks. Thus doses calculated are the mean doses in the given volume element. After tracking and tallying, a speci®ed number of independent number of histories is divided by the volume of the element and this gives the density of collisions per unit volume. Then the density value in each energy bin is divided by the width of the energy bin and by the total scattering cross-section averaged over the energy bin width. For simplicity of calculation it is intended to compute the neutron spectral distribution for two axial meshes at the most, i.e. in two disc slices. In each of the two slices the spectrum is obtained in ®ve radial multiplied by seven angular, i.e. 35 Space volumes. As it is well known that the Monte-Carlo method gives only approximate results, whether it is dose or spectrum. In case of spectrum results, if the statistics is poor, the volume elements for this purpose can be increased in size to increase the number of events in each volume elements thus improving the spectrum output. When the neutrons are incident on the body from the neutron source of de®nite spectrum as shown in Fig. 3 the dose received by the body varies from one position to another. The dose distribution in standard phantom of tissue equivalent material can be calculated by knowing the neutron spectrum at any certain point of interest.

Fig. 3. Neutron spectrum for (Pu±Be) neutron source.

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Fig. 4. Neutron distribution inside the tissue equivalent phantom at axial mesh =1 and angular mesh =1.

Fig. 5. Neutron distribution inside the tissue equivalent phantom at axial mesh =1 and angular mesh =4.

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Fig. 6. Neutron distribution inside the tissue equivalent phantom at axial mesh =2 and angular mesh =1.

Figs. 4±6 give same typical examples of calculated neutron spectrum distribution at the same selective points. The ®gures give the relation between the number of neutrons as a function of its corresponding energy. Fig. 4 gives this relation at axial mesh =1 and angular mesh =1 for radial meshes from 1±5, i.e. RM1,RM2,RM3,RM4, and RM5. It is clear from this ®gure the variation of the neutron spectrum from one point to another due to neutron inelastic scattering as well as radiative capture. The neutron spectra show continuous attenuation nearly in an exponential manner specially at thermal neutron energy ranges. But for fast neutrons this shows some variation. The reason for this discrepancies may be due to the variation of the neutron cross-section with respect to the target atoms in the tissue equivalent materials under investigation. Fig. 5 gives the neutron spectrum for axial mesh =1 and angular mesh =4 at radial meshes 2±5 and Fig. 6 gives the neutron spectrum for axial mesh =2 and angular mesh =1 at radial meshes 1±3. The distribution gives more or less the same trend as in Fig. 4 but of less intensity. This may be attributed to loss of neutron energy and hence the transfer of fast neutron to thermal neutron. This ®nally leads to the capture within the moderation medium. 3. Conclusion The intension of this work is to apply Monte-Carlo technique for derivation of the dose received by certain critical organ of man (skull) under accidental circumstances

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in case of horizontal reactor operation, or exposure to neutron source (of known spectrum). Despite of the diculties of application of such technique in computation of the dose received, yet, it may be of great help in assessing the neutron dose from neutron source of a de®ned spectrum. Moreover, some dosimetric information under conditions of sever exposure for certain positioning of occupational workers may be easily obtained by assessment of dose to skull. It should be born in mind that corrections for the turn over due to human recovery and blood circulation are required. References Cramer, S. et al., 1985. Los Alamos National Laboratory, N.M.CONF. 850411-12. Hurst, G., 1954. Brit.J.Radia. 27, 353. Iaslli, G., 1986. Nucl. Inst. Meth. 248, 488. Mottef, J. et al., 1963. Proc. of the Symp. on Neutron Dosimetry. IAEA, Vienna, p.213. Nagrajan, P., 1968. Proc. of the Regional Seminar on Radiation Protection Monitoring. IAEA, Bombay, p.61. Synder, W. et al., 1957. Brit. Journ. Radia. 28, 341.