Development of New Gamma-Ray Buildup Factor and Application to Shielding Calculations

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1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Development of New Gamma-Ray Buildup Factor and Application to Shielding Calculations Yoshiko HARIMA, Shun-ichi TANAKA, Yukio SAKAMOTO & Hideo HIRAYAMA To cite this article: Yoshiko HARIMA, Shun-ichi TANAKA, Yukio SAKAMOTO & Hideo HIRAYAMA (1991) Development of New Gamma-Ray Buildup Factor and Application to Shielding Calculations, Journal of Nuclear Science and Technology, 28:1, 74-84, DOI: 1.18/ To link to this article: Published online: 15 Mar 212. Submit your article to this journal Article views: 516 View related articles Citing articles: 13 View citing articles Full Terms & Conditions of access and use can be found at

2 journal of NucLEAR ScJEI\:CE and TECH:-IOLOGY, 28L1=. pp (january 1991). SUMMARY REPORT Development of New Gamma-Ray Buildup Factor and Application to Shielding Calculationsi Yoshiko HARIMA*l, Shun-ichi TANAKA*", Yukio SAKAMOTO*" and Hideo HIRAYAMA*" * 1 Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology *" Tokai Establishment, Japan Atomic Energy Research Institute * 3 National Laboratory for High Energy Physics Received August 13, 199 The PALLAS (discrete ordinates-integral transport) code was improved to include secondary sources, such as bremsstrahlung and fluorescence. to assure accurate and reliable results. The point buildup factors for high-z materials were calculated with this code in the energy range of.1515 MeV up to 4 mean free paths. The buildup factors for low-z materials in the low energy range, which are most difficult to calculate, were calculated with PALLAS and were validated by comparison with the results of the EGS4 (point Monte Carlo), and ANISN codes. A function to calculate coherent scattering was added to the EGS4 code. It was suggested that neglecting coherent scattering and assuming free-electron Compton scattering can result in an error in the buildup factor. A fitting formula. the geometric progression (G-P) form. was developed to reproduce the data in codes used for shielding design. This formula can reproduce the data over the full range of distance, energy and atomic number within a few percent. The above cited buildup factor data and the G-P formula have been adopted for proposed standard ANS "Gamma Ray Attenuation Coefficient and Buildup Factors for Engineering Materials". The G-P fitting function has been implemented in the CCC-493/QAD-CGGP and CCC-494/G33-GP codes available from the Radiation Shielding Information Center (RSIC) at Oak Ridge National Laboratory. These are used for r-ray shielding calculations throughout the world. Also. the data and the method of evaluation for 1 em dose equivalent, introduced into the japanese law according to ICRP recommendations, have been offered by this team. KEYWORDS: gamma-rag buildup factor, shielding, bremsstrahlung, fluorescence, coherent scattering, incoherent scattering, low Z material, low energy, MeV range, 4 mean free path, PALI,AS code, EGS4 code, reliability, G-P fitting formula, QAD-CGGP, G33-GP, I em dose equivalent, gamma-rag doses, ICRP I. INTRODUCTION Many shielding calculations for )'-rays in the nuclear facility have continued to rely on point-kernel methods incorporating a few buildup factor data calculated with the moments method by Goldstein & Wilkins and published in 1954''l for nearly 3 yr. But it lacks low-energy data, deep penetrating data, and data for many needed materials. Furthermore, it does not include secondary sources such as annihilation, fluorescence and bremsstrahlung. Over years, such data responding to the demands of various shielding calculation has! This article is a summary of the 22nd AESj Technical Award, No.229, (Apr.2, 199). * 1 -okayama. Meguro-ku, Tokyo 152. * 2 Tokai-mura, lbaraki-ken * 3 Oho, Tsukuba-shi

3 Vol. 28, No. 1 (Jan. 1991) Summary Report (Y. Harima et al.) 75 been requested. The 1979 accident at Three Mile Island (TMI) have served to emphasize the need of a comprehensive and reliable set of buildup factor. After accident, it was important to evaluate the activity of 131 Xe (it emits the most important r-rays at 8 kev), in the waste gas decay tanks and of noble gasses within the containment vessel. Dose rates had been measured by health physicists. However, to determine the activity in container, they needed r-ray attenuation data of low-energy that would predict the penetration of 131 Xe or noble gas r-rays through the container walls. The disposal of radiative waste should be quick and adequate, but it was interfered with the lack of low-energy data. Following the TMI accident, Working group ANS-6.4.3, developing a set of r-ray point-source buildup factors and attenuation coefficients for various engineering materials, set up by the American Nuclear Society Standard Committee in 198. One of authors, Harima, became a member of ANS-6.4.3, and all the authors worked hard together to develop the point buildup factor data. Before Working Group ANS was organized, a data base of buildup factors had already been in existence at the National Institute of Standards and Technology (NIST) for a number of materials(2). Though the NIST data base was rather comprehensive< 3 l<<l, the moment method calculations did not take into account either coherent scattering or the effect of bremsstrahlung generation and transport, and the importance of these effects had to be examined. In addition, there was an unknown uncertainty arising from the reconstruction of the moments. We contributed to Working group ANS with the following works: (1) The PALLAS (discrete ordinates-integral transport) code< l< l was improved to include the effects of secondary sources such as bremsstrahlung and fluorescence in the r-ray transport calculations, to assure accurate and reliable results. The point buildup factors for high Z materials were calculated with this code in the energy range of.15""'15 MeV, up to 4 mfp<7l-< l. (2) The buildup factors for low Z materials in the low energy range which are hard to calculate, were calculated' 1 ) with the P ALLAS< l and were assured by the comparison with the results of the EGS4 (point Monte Carlo) code< 11 l and the ANISN code' 12 l. (3) EGS4 was improved to do account for coherent scattering, and evaluated the effect by including both coherent and bound-electron incoherent scattering cross section in the low energy range' 13 ). ( 4) The fitting formula, the geometric progression (G-P) form' 14 )( 15 l was developed. This formula can reproduce the data over the full range of distance, energy and atomic number within a few percent. The G-P fitting function had been developed as an analysis and interpolation techniquec1 l. The G-P fitting function has been implemented in the QAD-CG and G33 codes and offered to RSIC. These are available from RSIC at Oak Ridge National Laboratory (ORNL), as the CCC-493/QAD-CGGP' 17 ) and CCC-494/ G33-GP' 18 > codes. These are used for the r ray shielding calculation in the world. ll. EFFECT OF SECONDARY SOURCES The improvement of the PALLAS code was performed by one of the authors, Tanaka, in cooperation with Takeuchi. At first, buildup factors including bremsstrahlung and annihilation radiation were calculated 9 2 H l for plane isotropic and plane normal sources using a discrete ordinates direct integration code, PALLAS-PL. Sp-Br< l. The PALL AS code treats the Klein-Nishina scattering cross section accurately. The validity of this code was checked by comparison with experiment' 2 'l and other calculation'22l. Next, buildup factors including bremsstrahlung were calculated' 23 l for a point isotropic source with the same code< l. The results were compared with those of moments calculations. The effect of bremsstrahlung on the buildup factor data is important for highz materials and for the higher source energies. Typical results are given in Table

4 76 Development of New r-ray Buildup Factor ]. Nucl. Sci. Techno/.. Distance (mfp) ( 1. 33) ( 5.46) (15.4) (61. 5 ) No bremsstrahlung in parenthesis Table 1 Bremsstrahlung effect on exposure buildup factor for a point isotropic source in Pb ( 1. 22) 8. 'ill ( 4. 'ill) 53.6 ( 3.) 1,31 (817 ) Energy (MeV) ,51 1 ( 1. 18) ( 4.7) ( 4 (2, 62 ) ) ( 1.16) 32.8 ( 4.3 ) 783 ( 81 ) 3,. (34, 8 ) Buildup factors including fluorescent radiation was calculated with the P ALLAS-ID (VB) code for a point isotropic sourcec J. At first, fluorescent radiation was treated with mean energy, 76.5 kev for Pbc 14 '. Continuously, the fluorescence effect was calculated in consideration of the 4 K X- raysc 7 H 8 ', using the photon cross section data taken from Hubbell's (NBS-29)c 2 "' and Storm & Israel's (DLS-15)c26J. Lastly buildup factor values for Mo, Sn, La, Gd, W, Pb and U were determinedc 9 > using the revised photon cross section data (PHOTX)c 27 '. Typical results are given in Table 2, R Table 2 Exposure buildup factor with fluorescence for Pb around K edge Energy (MeV) (mfp) El 2.94E E E E5 9.51E E5 6.43E1 2.36E Fig. 1 - PALLAS (DLC-151 EGS4 ASFIT 1 2 2!5 Penetration (mfpl Comparison of calculations by PALLAS (DLC-15), EGS4 and ASFIT codes for exposure buildup factors of Pb in case with and without bremsstrahlung for 1 MeV point isotropic source -76- Buildup factor values for Mo, Sn, La, Gd, W, Pb and U were determined with the PALLAS code, and validated by comparison with the results of the ASFITc 28 ' and EGS4 codes. Comparisons were shown in Fig. 1 for a case with or without bremsstrahlung in Pb at 1 MeV, and in Fig. 2 with or without K X-rays in Pb at.1 MeV. The photon cross sections were taken from DLC-15<"' for the PALLAS and EGS4 codes, and from NBS- 29<18' for ASFIT< 19 '. m. BUILDUP FACTORS FOR Low-Z MATERIAL AND FOR LOW ENERGIES Reconstruction of the flux density from the moments sometimes results in spurious oscillation. The G-P fitting function parameters were carefully analyzed, and buildup factor values which did not permit reasonable interpolation were replaced. In the low energy (.3-.3 MeV) values for Be, however, the NIST data oscillates

5 Vol. 28, No. 1 (Jan. 1991) Summary Report IY. Harima l'l a/.) 77 - PALLAS IDLC-15) EGS4 --- ASFIT... ti.. ;;:J ;g ;;:J CD ;;:J "'.. >< L1.J to' to 2 Penetration (mfp) Fig. 2 Comparison of calculations by PALLAS (DLC-15), EGS4 and ASFIT codes with or without K X-rays for.1 MeV point isotropic source strongly, and was impossible to be replaced with the above technique. So, buildup factors for a point source in infinite beryllium had been calculated in the low-energy range of _3"".3 MeV up to 4 mfp, using the PALLAS code<' '. The attenuation coefficient increases as the photon loses energy by successive scattering. There are circumstances, however, for which the total Compton cross section for the energies of the photon before and after the scattering changes infinitesimally at low energies and the photoelectric absorption cross section does not compete with the scattering process for low-z material. For such situations, the use of the uncollided components as the basis for the buildup factor results in an undesirably large value of the buildup factor. Although the basic physical principles governing such transport of photons were known many decades previously, it was only through the use of computers that these principles could be applied to photon shielding with high accuracy. Buildup factors for water have recently been calculated by the PALLAS code for low source energies<m. The results have been in good agreement with the results of the moments method. However, there are no reliable data for checking the buildup factor calculations by the PALLAS code for low source energies and for low-z materials except water. Buildup factors and energy spectra were calculated for Be with the PALLAS and -77-

6 78 Development of New r-ray Buildup Factor ]. Nucl. Sci. Techno!., ANISN codes and compared with those of the point Monte Carlo method EGS4 code. In the present problem, extremely fine angular, spatial and energy meshes are needed for the PALLAS and ANISN codes to obtain flux densities that are independent of the mesh size. The Be buildup factors by PALLAS were computed with the energy meshes of 12, and an isotropic quadrature set of 38 points. A point source was treated as uniformly distributed in the spherical shell with a radius of.1 em. The same buildup factors were calculated with the energy meshes of J4 1 3 Point isotropic source Beryllium L_ I ANISN-JR E =.1 MeV. 1 EGS4 PALLAS 1 by ANISN, using an S 38 P 5 approximation. The EGS4 code had a lower energy limit of 1 ke V for photons. In the calculation with EGS4 1, case histories were used. The first comparison with EGS4 results for normal incident source is performed for validity of discretization of the angular, spatial and energy variable, and the second one with EGS4 results for a point source for that of substitution of a small spherical shell sources for a point source. Energy spectra from a point isotropic source of.1 MeV in Be are compared in Fig. 3, and buildup factor for a point source,..._... ::t.... c... X (!) N....q J2..,. X ::J ;;: >. '.... (!) c:: w 1 o' 1 -L Gamma-ray energy(mev) Fig. 3 Comparison of energy spectra from a point isotropic source of.1 MeV in Be, using different calculation codes -78-

7 Vol. 28, No. 1 (Jan. 1991) Summary Report (Y. Harima et a!.) 79 of.1 MeV are compared in Table 3. Table 3 Comparison of exposure point buildup factors for Be at.1 MeV R (mfp) PALLAS ANISN EGS ± E3 7.15E3 9.68E3±4.29E E E E E6 Both PALL AS and ANISN are discrete coordinates codes, but they adopt different methods for the treatment of the scattering process. However, both results up to 1 mfp are in good agreement for a point source with those of EGS4. W. EFFECT OF COHERENT SCATTERING There is a statement in the literature that coherent scattering can be neglected for most shielding calculations under the condition that the total attenuation coefficient used to the calculations does not include it, since there is essentially no energy change and only a small change in direction with coherent scattering. This is true only for photons above a few hundred kev. The probability that the photon is scattered by a large angle increases below a few hundred ke V, especially for a high Z material. Furthermore, Compton scattering should not be treated as scattering with a free electron in this energy region, but must take into account the binding correction (incoherent scattering). One of the authors, Hirayama, participated in the improvement of an electron-r -ray shower Monte Carlo code EGS4 added a faculty to be able to calculate coherent scattering to it. Calculations for water, Fe and Pb have been reported by Hirayama & Trubey< 1 '\ as correction factors to the usual buildup factors that do not include coherent scattering. The correction factor is the ratio of a "pseudo" buildup factor (coherent, bound) to the "true" buildup factor (without coherent, free electron) and both buildup factors are evaluated at the same distance in centimeters. Ratios for water, Fe and Pb at 6 ke V are plotted as a function of distance in Fig. 4, and those at 1 mfp as a function of photon energy in Fig v 1.3 cc... "' 1.2 '2 I. I i3 "".c 1..u cc Q9 1.2 u 1.1 CD "' "C c= ::> "".u ""'.9.8 cc v 1. CD... "'.9 ].8 "" 7.u CD.6 - Wa1er 5 Pene1ra1ion, mfp Iron Lead Fig. 4 Ratios of pseudo exposure buildup factor with coherent and bound electron Compton scattering to true one without coherent and free electron Compton scattering for water, Fe and Pb at 6 key The pseudo buildup factor differs from the true buildup factor because of an inconsistency in the cross sections used for the scattered and uncollided doses. It can be observed that these corrections can either increase or decrease the dose calculated from the standard buildup factors. V. FITTING FUNCTION Although some analysts prefer to use a data table directly in computer calculations, others prefer parameterized forms. Over the years a number of functional forms have been used to parameterize buildup factor data, in particular, the Taylor<' ' and Berger's< 81 ' fitted Goldstein & Wilkins data. For the new data extended up to lower source 1-79-

8 8 Development of New ;--Ray Buildup Factor ]. Nuc/. Sci. Techno! Water Q9 1.2 "' 1.1.., co "' 1...._ :g :=.t::.7 -.., co 1.1 Lead Pho1on Energy ( kev l Fig. 5 Ratios of pseudo exposure buildup factors with coherent and bound electron Compton scattering to true ones without coherent and free electron Compton scattering at 1 mfp penetration depth as a function of photon energy for water, Fe and Pb energies and deeper penetrating length, accuracy of these forms is a problem for a low-z materials and low energies. It is now clear that the best available form is the geometric progression (G-P) form. This formulacl'j is expressed as, B(E, x)=1+(b-l)(l\i -1)/(K---1) for K=l=1 =1+(b-1)x for K =1, ( 1) K (x)=cxa +d[ { tanh(x/ Xk -2)-tanh( --2)} /{1-tanh(-2)}], (2) and accurately represents the buildup factor data as a function of distance for the following reasons: (1) The value of parameter b corresponds to that of the buildup factor at 1 mfp, which Is the integration of a basic spectrum for a specified material and a specified source energy. (2) The variation of parameter K with penetration represents the photon dose multiplication and the change in the shape of the spectrum. This formula can accurately reproduce the data over the full range of energy and atomic number within a few percent. For example, the maximum deviation to.15"'15 MeV, up to 4 mean free paths of water for the exposure buildup factor is 3%. In contrast of this, Taylorc' J is 53.2%, and Bergerc' 1 J 42.7 %c J, where the parameters of these formulas were fitted to the values for the thickness 2"'4 mfp of the basic data. Reconstruction of the flux density from the moments sometimes results in spurious oscillation. The G-P fitting function parameters were carefully analyzed and buildup factor values which did not permit reasonable interpolation were replaced with the following method. Omitting several of the 16 data points for water at.1 MeV and fitting parameters of the G-P formula to the remaining data, the G-P parameters thus obtained reproduce within 1% the omitted data pointscl'j. The variation of each parameter with respect to loge is smooth. In order to obtain the values for an arbitrary energy, the parabolic interpolation of each parameter with respect to log E was adopted. The validity to interpolate the parameters of the G-P form in loge was confirmed from the comparison of interpolated results at E.=.66, 1.25, 3.5 and 9 MeV in water with those of the Capo forme'"). The results agree within l%c 1 'J. Furthermore confirmation was obtained from the comparison of the results for.1 MeV interpolated from.6,.8,.15 and.2 MeV with.1 MeV in water, which gave good agreement within 1q-Cl"J. Some questionable values in the basic data were replaced with evaluated data by using interpolating technique for parameters of the G-P formula in penetrating distance and in photon energyc:m. --8-

9 .. Vol. 28, No. 1 (Jan. 1991) Summary Report (Y. Harima et al.) 81 The values of the G-P fitting parameters are given for basic data of.5"'4 mfp. However, it is not sure whether these parameters permit extrapolation to deep penetration above 4 mfp. Some typical buildup factor data up to 11 mfp were calculated for water, concrete, Fe and Pb by the PALL AS code. The extrapolated results with use of the parameters fitted to the calculated data up to 4 mfp to the calculated data above 4 mfp could not exactly reproduce the basic data above 4 mfp, because the sensitivity of the parameter K becomes severe as the distance increases. Here, one of the authors, Sakamoto, proposed an extrapolation of the function K(E, x)< > for deep penetration above 4 mfp as follows: K K(E, x)=ks,( K:: ) K,;; ,;;1 (') 3 - K ' t;<x)frn where (x/35) 1-1 (X)= (4/35) 1-1 K 36=K(E,35), fm=o.b K 4=K(E,4). ( 4) For elements not listed in the ANS data, buildup factors can be determined by interpolation of the G-P parameters in atomic number. For the mixture and compounds, an equivalent atomic number can be estimated from the ratio of the scattering cross section to the attenuation coefficient. The values of the equivalent atomic number for each mixture are divided into two values for energy either below or above 1.5 MeV. These phenomena can be explained by the fact that in the energy range below 1 MeV, the photoelectric effect with z dependence is dominant, and the pair production with Z 2 dependence has a photon threshold energy of 2m,c 2 (=1.2 MeV) and becomes dominant with increasing photon energy< '>. The equivalent atomic number of various media are listed in Table 4, together with their composition. Medium Air Water Density (g/cm 2 ) Table 4 Equivalent atomic number of various media NBS FP-a Lucite Polyethylene concrete concrete (C,Hs2)n (C,H,) n Composition (Weight fraction) H Olll c N Na.171 Mg AI Si p.27 s.12 Ar. 13 K Ca Cr.5 Mn.25 Fe Equivalent atomic number E<l. 5 MeV E>l. 5 MeV Sand

10 82 Development of New r-ray Buildup Factor ]. Nucl. Sci. Techno!., For source energies above the mtmmum in the total cross section, the interpolation of buildup data remains a problem for mixtures that include a heavy component (the correct buildup factors for lead glass were given in Ref. (l$). For high-z materials, the buildup factors near shell edges can become very large due to the non-continuous nature of the cross sections. This can be observed in the values for molybdenum and elements of higher Z. Discussions of this phenomenon are contained in Ref. (34). It should be kept in mind that fluctuations of the attenuation factor (B(E, x)e-'"") are not nearly as great as that of the buildup factor. Thus, for energies just above the K edge, interpolation in the attenuation factor is easier than in the buildup factorc 34 J. The G-P fitting has been implemented in the CCC-493/QAD-CGGP and CCC-494/ G33-GP codes available from RSIC at ORNL. When these data are incorporated in other codes, the buildup factor are available in computer-readable form from RSIC at ORNL as DLC-129/ ANS-6.4.3c J. VI. 1 em DOSE EQUIVALENT FOR PHOTONS BEHIND SHIELD MATERIAL The 1 em dose equivalent (H(lO)), which is the dose equivalent at 1 em depth of ICRU sphere, was used as the effective dose equivalent for external exposure in the revised radiological protection law. It was also decided that H(1) in the practical field was evaluated with the ambient dose equivalent (H*(1)). The H*(lO) can be calculated from the photon flux with the 1 em dose equivalent conversion factor. However, the discussions concerning H(1) were limited to that in the free space. H*(lO) in the free space is always larger than H(1). Hirayama & Tanaka investigated the relation between the absorbed dose of plane phantom behind the shield and H*(1) at the surface of human body behind the shielding materials of water, concrete, Fe and Pb by using the EGS4 code. The applicability of the average conversion factors and practical conversion factors calculated with the EGS4 and PALLAS codes was investigated as the practical method to evalute H*(1) with the point kernel calculation. Average exposure to 1 em dose equivalent conversion factor H*(lO)= J, em X, where H* (1) and X (finite) : Sv and R units, respectively ] 1cm: Average exposure to 1 em dose equivalent conversion factor ( 5) Practical exposure to 1 em dose equivalent conversion factor H*(1)= J p, 1 cmxinf' ( 6) ]p,lcm: Practical exposure to 1 em dose equivalent conversion factor X;nf: Exposure in infinite medium. It is possible to evaluate H*(1) in safety side by using the maximum practical conversion factor beyond 1 mfp for each material, depending only the energy of incident photons. Figure 6 shows maximum practical conversion factors calculated with PALL AS between 1 and 3 mfp for water, concrete, Fe and Pb, together with exposure to 1 em dose equivalent conversion factor as a function of incident photon energy. It was confirmed that both conversion factors for a point isotropic case are almost the same with those for a plane geometry from the calculation by EGS4 and PALLAS. Both conversion factors for absorbed dose of air (Gy) to ambient dose equivalent are obtained by those multiplied by l15c' 7 l. The maximum practical conversion factor has already been implemented in the QAD CGGP2 and G33-GP2 codesc J and they are available from NEDAC (Nuclear Energy Data Center). VH. SUMMARY Codes using point kernel method are very popular, because those are easily treated, independent of a person dealing with, and giving the calculated result of the same accuracy as an advanced transmission calculation except a special complex geometry. -82-

11 Vol. 28, :'\o. 1 (Jan Summary Report 1Y. Harima ct a/.) 83 I a: > (f)... e -- - Q. xior 2 ---r--,-.-r---o-,-rrrrn 1.5 l X "' Water Concrete Iron... Lead 1. a "' 6 6"' "' "' X... l X I I em.l.l X! s "' "'! Incident Photon Energy (MeV l Fig. 6 Maximum practical exposure to 1 em dose equivalent conversion factors between 1 and 3 mfp. and exposure to 1 em dose equivalent conversion factors as a function of incident photon energy The accuracy of the point kernel method is only depend on that of the buildup factor data. In order to supply lacked data unsuitable means were in use< 38 '. We carefully examined them < 39 '. We supplied correct buildup factor data, including secondary sources, and for low Z material and low energies. We suggested that neglecting coherent scattering and assuming free electron Compton scattering can result in an error in the buildup factor. The G-P fitting formula made possible to calculate the value of buildup factor for an arbitrary material, energy, and penetrating length over the whole range. The maximum practical conversion factor already is used for r-ray shielding calculation implementing in the QAD-CGGP2 and G33-GP2 codes. These processes were explained in Ref. (4). The 1988 draft Standard was published as ORNL/RSIC-49 and the new buildup factor data is available from RSIC as DLC-129/ ANS The last data will be not long incorporated into the standard. ACKNOWLEDGMENTS The authors are greatly indebted to D. K. Trubey, Chairman ANS-6.4.3, for many fruitful discussions and suggestions. They would like to express their gratitude to K. Takeuchi, with whom the PALLAS code was originated, for development of the PALLAS code. They also wish to thank Members of Nuclear Power Code Committee, Sub W. G. Simple Calculation Evaluated Group, and Research Committee on Shielding of Radiation Facilities, Buildup Factor Sub-committee, for their variable discussions. II) GoLDSTEIN, H.. WILKI:-;s, J. E.:,VY-375. (1954). (2) TRUBEY, O.K.: Proc. 6th Int. Conf. Radia. tion Shielding, 1241 (1983). (3) EISENHAUER, C. M., SIMMONS. C. L. : N uc/. Sci. Eng., (1975). -REFERENCES- -83-

12 84 Development of New r-ray Buildup Factor ]. Nucl. Sci. Techno/., (4) CHILT:'-1, A.B., EISENHAUER, C.M., SiM"viONS, C. L.: ibid., 73, 97 (198). (5) TAKEUCHI, K., TANAKA, s.: PALLAS-PL, SP Br; A code for direct integration of transport equation in one-dimensional plane and spherical geometries, ]AERI-M 9695, (1981). (6) idem.: PALLA-lD (VII), A code for direct integration of transport equation in one-dimensional plane and spherical geometries, ]AERI M , (1984). (7) SAKAMOTO, Y., TANAKA, S., HARIMA. Y.: Data library of gamma-ray buildup factors for point isotropic source-molybdenum, tin, lanthanum, gadolinium, tungsten, lead. and uranium, ]AERI-M 87-21, (1988). (8) idem. : Interpolation of gamma-ray buildup factors in atomic number, using the geometric progression (G-P) parameters, ]AERI-M 88, (1988). (9) SAKAMOTO. Y., TA:--IAKA, s.; QAD-CGGP2 and G33-GP2; Revised versions of QAD-CGGP and G33-GP code with conversion factors from exposure to ambient and maximum dose equivalents, ]AERI-M 9-11, (199). M HARIMA. Y., HIRAYAMA. H., IsHIKAWA, T., SAKAMOTO, Y., TA:-<AKA, S.: Nucl. Sci. Eng., 96, 241 (1987). (II) NELS:'-1, w. R., HIRAYAMA, H.. ROGERS. D. W..: EGS4 code system, SLAC-265, (1985). (1 KoYAMA, K., et a/: ANISN-JR; A one-dimensional discrete ordinates code for neutron and gamma-ray transport calculation, ] AER I.M 6954, (1977). (1l HIRAYAMA, H., TRL"BEY, D. K.: Nucl. Sci. Eng.. 99, 145 (1988). (1 HARIMA, Y.; ibid., (1983). a$ HARn1A, Y., SAKAMOTO, Y., TA:-<AKA, S., KAWAI, M.; ibid., 94, 24 (1986). (!$ HARIMA, Y., et a/. : Applicability of geometric progression approximation (G-P method) of gamma-ray buildup factors, ]AERI.M 86-71, (1986). (1 ORNL: RSIC computer code collection, CCC. 493, (1986). M ibid. : CCC-494, (1986). M TAKEUCHI, K., TANAKA, S., KIN'<O, M.: Nucl. Sci. Eng., 78, 273 (1981). g TAKEUCHI, K., TANAKA, s.; ibid., 87, 478 (1984). 1) BISHOP, G. B., SMITTON, C., PACKWOOD, A.; Ann. Nucl. Energy, 3, 65 (1976). ]lang, S. H. : Nucl. Sci. Eng., 75, 16 (198). l TAKEUCHI, K., TANAKA, S. : ibid., 9, 158 (1985). (Z TANAKA, S., TAKEUCHI, K.; ibid.. 93, 376 (1986). (2$ HUBBELL, J. H.; NSRDS-NBS 29, (1969). (2$ STORM, E., IsRAEL, H.l.: Nucl. Data Tables, A7, 565 (197). (2 Radiation Shielding Information Center Data Package DLC-136/PHOTX; Photon Interaction Cross Section Library, Contributed by NIST. tz$ Radiation Shielding Information Center Data Package CCC-336/ ASFIT-V ARI, Gamma-Ray Transport Code for One-Dimensional Finite Systems, Contributed by Indira Gandhi Center for Atomic Research, India. tz HIRAYAMA, H., TANAKA, s., SAKAMOTO, Y., SuBBAIAH, K. V., HARIMA, Y.: ]. Nucl. Sci. Techno/., 27[5], 524 (199). (ll) TAYLOR,].].; WAPD-RM-217, (1954). (ll) BERGER, M. ]. : USNRDL Reviews and Letures, No. 29, p. 47 (1956). (l CAPO, M.A.; APEX-51, (1958). ill TRUBEY, D. K.: ORNL/ RSIC-49, (1988). \l HARIMA, Y., TRUBEY, D. K., SAKAMOTO, Y., T A<"AKA, S. : To be published in Nucl. Sci. Eng., (1991). \l$ SAKAMOTO, Y., TANAKA. S., HARD,IA, Y.; Nucl. Sci. Nng., 1, 33 (1988). \l$ Radiation Shielding Information Center Data Package DLC-129/ ANS643, Geometric Progression Buildup Factors and Attenuation Coefficients, Contributed by ANS Standards Working Group ANS The package was assembled by D. K. Trubey from computer-readable files transmitted from Japan by Y. Sakamoto. (l HIRAYAMA, H., TANAKA, S.: ]. At. Energy Soc. ]pn., (in japanese), 31 [7], 841 (1989). \l$ WALKER, R. L., GROTENHUIS, M.; ANL-6443, (1961). (l Exposition by Research Committee on Shielding of Radiation Facilities; Buildup Sub-Committee : Current status and future scope of gamma-ray buildup factor, ]. At. Energy Soc. ]pn., (in Japanese), 3[5], 385 (1988).!) HARIMA, Y., TANAKA, S., SAKAMOTO, Y., HIRAYAMA, H, ; ibid., 31 [ 4], 477 (1989). -84-