A. Shirani*and M. H. Alamatsaz

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1 IJST (013) A1: 9-34 Iranian Journal of Siene & Tehnology Calulion of exposure buildup fators for point isotropi gamma ray soures in strified spherial shields of wer surrounded by lead and optimizion of wer-lead ombinion A. Shirani*and M. H. Alamsaz Department of Physis, Isfahan University of Tehnology (IUT) P.O. Box: , Isfahan, Iran Abstrat Exposure buildup fators have been aluled by Monte Carlo method for point isotropi gamma ray soures, penetring a two-layer spherial shield of wer surrounded by lead, and the effet of bremsstrahlung radiion on buildup fators has, in partiular, been investiged, the results of whih are in good agreement with previous works. The buildup fators were then aluled for various ombinions of wer and lead layers some gamma ray energy points in the range from 0.04 MeV to 10 MeV and for shield thiknesses from 1 to 10 mean free phs (mfp). From the results obtained, one an selet the proper (or optimum) wer and lead ombinion whih results in minimum value of buildup fator for a two-layer wer-lead shield of a given thikness (in mfp) eah energy point. Here the optimizion analysis has been performed for a shield of 10 mfp thik gamma ray energies from 0.04 MeV to 10 MeV. Keywords: Strified shields; Monte Carlo simulion; buildup fators; bremsstrahlung radiion 1. Introdution The photon build up fator is defined as the rio of the total photon beam response (e.g., flux, dose or exposure) to the response of the unollided photon beam fration. Buildup fators whih aount for multiple stering of photons and seondary soures of annihilion, fluoresene and bremsstrahlung radiion are basi da for point kernel methods th are used in gamma-ray shielding and dosimetry alulions. The buildup fator an be obtained, in priniple by experiment, but sine the tenuion oeffiients and stering ross setions are known with reasonable auray, buildup fators are ustomarily obtained either by solution of the photon transport equion or by Monte Carlo method. A detailed historial review on build up fator alulion and use is given by Harima [1]. Although buildup fators have been widely aluled and used for mono-layer shields [-8], they have also been onsidered for multilayer shields [9-14]. In this work, a Monte-Carlo program was written to simule the transport of gamma rays through mter and to alule the exposure buildup fators for a point mono-energeti isotropi gamma ray soure loed the enter of a strified spherial *Corresponding author Reeived: 19 Deember 010 / Aepted: 17 November 01 shield of wer (as a low Z-value merial) surrounded by lead (as a high Z-value merial). We began our study by taking into aount oherent and inoherent sterings and investiged the effets of these phenomena on buildup fators up to gamma ray energies of 3 MeV, the results of whih were published in ref. [14]. In the present work we ompleted the program by taking into aount seondary soures of bremsstrahlung and aluled the buildup fators up to gamma ray energies of 10 MeV. The (infinite-medium) buildup fators were aluled for various ombinions of wer and lead layers some gamma ray energy points in the range from to 10 MeV and for shield thiknesses from 1 to 10 mean free ph (mfp). In order to onsider the infinite medium ondition in the program, total thikness of the shield was taken to be 13 mfp (th is 3 mfp more than the maximum distane onsidered in the alulions). From the results obtained, one an selet the proper (or optimum) wer and lead ombinion whih results in minimum value of buildup fator (and therefore in minimum value of gamma ray exposure) for a shield of given thikness (in mfp) eah energy point. Here, the optimizion analysis has been performed for a shield of 10 mfp thik gamma ray energies from to 10 MeV. It is to be noted th for a shield of (say) 10 mfp thikness, the intensity of unollided photon beam is tenued

2 IJST (013) A1: exponentially by a fator of e -10 and is independent of shield merial ombinion, but the total beam response is merial-ombinion dependent and is minimum when the buildup fator is minimum. Other limitions like spae and merial weight are of ourse of speial importane whih should also be taken into onsiderion in pratie.. Method of alulion The method of alulion is fully desribed in (our previous paper) ref. [14]. The ross-setions used were taken from ref [15]. The type of interations onsidered in the program are: photoeletri, inoherent stering (whih is Compton stering onsidering binding effets of eletrons), oherent (Rayleigh) stering and pair prodution. Fluoresene and bremsstrahlung radiions are also taken into aount. As the main objet of this study was to onsider the effet of bremsstrahlung radiion on buildup fator, in the following setion a brief desription of the formulas onerning bremsstrahlung radiion is given. 3. Bremsstrahlung radiion In the ase of gamma-ray transport, the bremsstrahlung soures are photo eletrons, Compton eletrons and eletrons and positrons of pair prodution. When an eletron (or positron) with kineti energy E passes through a medium with omi number (or a ompound with effetive omi number) Z, the rio of stopping power due to radiion to th due to ollision is approximely given by [16]: de dx de dx r EZ r. 750 (1) For suh an eletron, the probability of bremsstrahlung emission is therefore: de dx r r P. de de r 1 dx dx r () A simple desription of the bremsstrahlung differential ross setion (DCS) is provided by the Bethe Hitler formula with sreening. The Bethe Hitler DCS for bremsstralung emission by eletrons (or positrons) in the field of an om of omi number Z and sreening radius R an be expressed as [17]: BH dbr 1 4 r Z(Z ) (b) (1 ) (b) (3) e 1 dw w 3 where is the fine struture onstant, r e is the lassial eletron radius, w is the energy of the emitted photon, and w E me w, me E 1 me R me 1 b 1 φ1b4lnrme/ ln1b 4bartanb 1, (4) φb4lnrme/ 7 3 ln1b 6bartanb 1 (5) 1 b 4 4b artan ( b ) 3ln (1 b ). The quantity in eq. (3) aounts for the prodution of bremsstrahlung in the field of the omi eletrons; in the high energy limit ~1.. To simule the emission of bremsstrahlung radiion in the program, an eletron (or positron) with kineti energy E was assumed to radie bremsstrahlung photons with a probability given by eq. (). Z was taken to be 8 for lead and 7. for wer. The energy of the emitted photon (w), whih takes values in the interval 0 to E, was seleted from distribution (3) by means of random numbers and the rejetion sampling tehnique. The redued sreening radius, R m e / was taken to be 3.9 for lead and 100 (whih is the weighted mean value for two hydrogen om and one oxygen om) for wer [17]. Bremsstrahlung photons were produed the position of the eletrons (or positrons) and were emitted in diretions of eletrons (or positrons), as in the disrete ordine ode, PALLAS [18]. The diretions of Compton eletrons were determined from Compton formulas and the diretions of photo eletrons and pair reion eletrons (or positrons) were in the diretion of the photon th aused the proess. 4. Results and Disussion 4.1. Comparison with previous works Using the point Monte Carlo ode EGS4 [19], Harima and Hirayama [9] have aluled exposure buildup fators for a two-layer shield of 5 mfp wer followed by 8 mfp lead, for gamma ray energies between 0.1 and 10 MeV. In our previous work, ref. [14], we have shown th under similar

3 31 IJST (013) A1: 9-34 onditions our results are onsistent with those of ref. [9] up to gamma ray energies of 3 MeV. Here in Fig. 1 we have ompared our results with those of ref. [9] 10 MeV gamma ray energy, where bremsstrahlung has signifiant effet on buildup fators. It is seen th the two results are onsistent (with maximum disrepany of less than 10 perent whih ould be due to small differenes in the method of alulion in the two programs) and it ould therefore be onluded th our program produes buildup fators with reasonable auray to be used for shielding designs. In addition, in the speial ase where wer layer was taken zero and the shield was therefore onsidered to be lead alone, our two layer program, with bremsstrahlung radiion inluded, resulted in exposure build up fators onsistent with those of mono layer lead shields of ref. [8]. This omparison is shown in Table 1. The buildup fators presented in this Table have been aluled (in lead medium) for both ases with and without bremsstrahlung radiion taken into aount, and in partiular show the effet of bremsstrahlung radiion on buildup fators. It is seen th bremsstrahlung radiion inreases the buildup fators all distanes from the soure and the effet inreases with distane, suh th a distane of 10 mfp distane, the buildup fator with bremsstrahlung radiion is almost three times th without this radiion. Fig. 1. Gamma ray exposure buildup fators versus shield thikness(in mfp) for a two-layer shield of 5 mfp wer followed by 8 mfp lead and omparison with those of ref. [9] 10 MeV gamma ray energy Table 1. Comparison of exposure buildup fators with those of ref [8] 10 MeV gamma ray energy for a single layer shield of lead various distanes (in mfp) from the soure. Comparison has been made for both ases with and without bremsstrahlung radiion taken into aount mfp This work with brem This work without brem PALLAS with brem PALLAS without brem EGS4 with brem EGS4 without brem Exposure Buildup fator values. With all types of gamma ray interations (inluding bremsstrahlung radiion) onsidered in our program, exposure buildup fators were aluled for various ombinions of wer and lead layers some gamma ray energy points in the range from to 10 MeV and for shield thiknesses from 1 to 10 mfp. These fators, whih are given in Table an be used in alulions of gamma ray transmissions through suh shields. These results ould also be used to develop formulas, similar to those of ref [13], for aluling exposure buildup fators for two layer shields in general Optimizion of buildup fators. The buildup fators 10 mfp distane from the soure, given in the first setion of Table, are plotted versus wer thikness, in mfp, various gamma ray energy points from to 10 MeV in Fig. ( eah point the rest of the shield is lead). It is seen th gamma ray energies below~0.5 MeV, where the photo eletri effet is dominant, buildup fator is minimum when wer layer is zero and the shield is hosen to be lead alone. From~0.5 MeV to~3 MeV, where Compton stering is dominant, the buildup fators are minimum up to about 4 mfp wer and no signifiant variion is observed. At 4 MeV any ombinion of wer and

4 IJST (013) A1: lead ould be hosen without any signifiant variion in buildup fator values. Above 5 MeV, where the bremsstrahlung is signifiant the proess is reversed and the buildup fator is minimum when above 7 mfp is taken to be wer. At 10 MeV the buildup fator is minimum when the whole 10 mfp is taken to be wer. Table. Exposure buildup fators various distanes (in mfp) from the soure for different thiknesses (in mfp) of wer and lead some gamma ray energies Wer-lead (mfp) 40 kev 00 kev 1 MeV MeV 3 MeV 6 MeV 10 MeV 10 mfp 9 mfp 8 mfp 7 mfp 6 mfp 5 mfp 4 mf 3 mfp mfp 1 mfp

5 33 IJST (013) A1: 9-34 Fig.. Exposure buildup fators 10 mfp distane from the soure versus wer thikness. At eah point the rest of the shield thikness (i.e. 10- r ) is made of lead

6 IJST (013) A1: Conlusion In this work, exposure buildup fators were aluled by Monte Carlo method for point isotropi gamma ray soures loed the enter of a strified spherial shield of wer surrounded by lead. All types of gamma ray interations inluding photoeletri, oherent stering, bound-eletron Compton stering, annihilion gamma rays, fluoresene and bremsstrahlung radiions were onsidered in the alulions. The exposure buildup fators were aluled for various ombinions of wer and lead layers some gamma ray energy points in the range from 0.04 to 10 MeV and for shield thiknesses from 1 to 10 mfp, whih ould be used in designing suh shields for gamma ray soures. The buildup fators 10 mfp distane from the soure were analyzed some gamma ray energy points to obtain the optimum wer-lead ombinion whih results in minimum buildup fator value this distane. The general feures of the analysis show th low gamma ray energies ( E <0.5 MeV) where photoeletri effet is dominant, the best ombinion is zero mfp wer -10 mfp lead (lead alone), intermedie energies (1 MeV< E <3 MeV) where Compton stering is dominant 5 mfp wer-5 mfp lead (half wer-half lead) ould be taken as optimum ombinion, and finally E =10 MeV where bremsstrahlung is dominant in lead the best ombinion is 10 mfp wer- zero mfp lead (wer alone). The buildup fators presented in Table show th this general behaviour is seen other distanes from the soure. Aknowledgments This work was supported by Isfahan University of Tehnology under projet 1PHA80. Sinere thanks of the authors are due to the Researh Counil of the University. Referenes [1] Harima, Y. (1993). An historial review and urrent stus of buildup fator alulions and appliions. Radi. Phys. Chem., 41, 631. [] Eisenhauer, C. M. & Simmons, G. L. (1975). Point isotropi gamma-ray buildup fators in onrete. Nul. Si. Eng., 56, [3] Chilton, A. B., Eisenhauer, C. M., & Simmons, G. L. (1980). Photon point soure buildup fators for air, wer and iron. Nul. Si. Eng., 73, [4] Takeuhi, K. & Tanaka, S. (1985). Point isotopi buildup fators of gamma rays, inluing bremsstrahlung and annihilion radiion for wer, onrete, iron, and lead. Nul. Si. Eng., 90, [5] Kitsos, S., Assad, A., Diop, C. M. & Nimal, J. C. (1994). Determinion of point isotropi buildup fators of gamma rays inluding inoherent and oherent stering for aluminum, iron, lead and wer by the disrete ordines method. Nul. Si. Eng., 117, 46. [6] Shimizu, A. (00). Calulion of gamma-ray buildup fators up to depths of 100 mfp by the method of invariant embedding. Journal of Nul. Si. and Tehnology, 39, [7] Alamsaz, M. H. & Shirani, A. (00). Calulion of point isotropi buildup fators of gamma rays for wer and lead. Iranian Journal of Physis Researh. 3(1): 7. [8] Hirayama, H., Tanaka, S., Sakamoto, Y., Subbaiah, K. V. & Harima, Y. (1990). Comparison of gamma-ray point isotropi buildup fators inluding fluoresene and bremsstrahlung in lead using disrete ordines and point Monte-Carlo methods. Journal of Nul. Si. and Tehnology, 7(6), [9] Harima, Y. & Hirayama, H. (1993). Detailed behavior of exposure buildup fator in strified shields for plane normal and point isotropi soures, inluding the effets of bremsstrahlung and fluoresent radiion. Nul. Si. Eng., 113, [10] Shin, K. & Hirayama, H. (001). Calulion of gammaray buildup fators for two-layered shields made of wer, onrete and iron and appliion of approximing formula. Radi. Phys. Chem., 61, [11] Su, M. F. & Jiang, H.S. (1989). Gamma ray buildup fators for a point isotropi soure in strified spherial shields. Nul. Si. Eng., 10, [1] Assad, A., Chiron, M., Nimal, J. C. & Dip, C. M. (1999). A new approximing formula for aluling gamma-ray buildup fators in multilayer shields. Nul. Si. Eng., 13, [13] Gurendik, M. & Tsoulfanidis, N. (000). Formulas giving buildup fator double-layered shields. Nul. Teh., 131. [14] Alamsaz, M. H. & Shirani, A. (00). A study of gamma ray exposure buildup fators in strified shields for point isotropi soures, inluding the effets of inoherent and oherent stering. Journal of Sienes, Islami Republi of Iran 13(3), [15] [16] Tsoulfanidis, N. (1995). Measurement and detetion of radiion. Taylor and Franis, 130. [17] Salv, F., Fernandez, J. M. & Sempau, J. (003). PENELOPE, a ode system for Monte Carlo simulion of eletron and photon transport. page [18] Takeuhi, K., Tanaka, S. (1984). PALLAS-1D (VII), A ode for diret integrion of transport equion in onedimensional plane and spherial geometries, JAERI-M [19] Nelson, W. R., Hirayama, H., Rogers, D. W. O. (1985). EGS4 ode system, SLAC-65.

SHIELDING MATERIALS FOR HIGH-ENERGY NEUTRONS

SHIELDING MATERIALS FOR HIGH-ENERGY NEUTRONS SHELDNG MATERALS FOR HGH-ENERGY NEUTRONS Hsiao-Hua Hsu Health Physis Measurements Group Los Alamos National Laboratory Los Alamos, New Mexio, 87545 USA Abstrat We used the Monte Carlo transport ode Los