Approximating Model for Multilayer Gamma-Ray Buildup Factors by Transmission Matrix Method: Application to Point Isotropic Source Geometry

An approximating formula recently proposed by the authors for gamma-ray buildup factors of multilayered shields is applied to point isotropic source problems. The formula, which is formulated in vector form with a four-group approximation, handles the gamma-ray energy spectrum directly and uses the transmission and albedo matrices to take gamma-ray transmission and backscattering effects into consideration. The gamma-ray transmission and back-scattering probabilities through a 1-mean-free-path- (mfp-) thick shell depend on the shell curvature. This phenomenon plays an important role in simulating the gamma-ray buildup factor in point isotropic source geometry. In this model, the dependence is described by simplified expressions. The feasibility of the formula for systematically describing the point isotropic buildup factors was tested by using buildup factors calculated by the Monte Carlo method as reference data. The materials used in the tests were water, iron, and lead, and the source energies assumed were 0.5, 1, and 10 MeV. Through the tests, the method was found to reproduce the reference data of double-layered shields of these materials very well. With the same parameters, the buildup factors of three-layered shields are also reproducible. Buildup factors computed with two different group structures were examined to test the adequacy of the energymore » group structure adopted. The group structure previously adopted was found to be adequate in the energy range of 0.5 to 10 MeV.« less

[1]  H. Hirayama,et al.  A new approximating model for gamma-ray buildup factors of stratified shields , 1994 .

[2]  J. C. Nimal,et al.  Determination of Point Isotropic Buildup Factors of Gamma Rays Including Incoherent and Coherent Scattering for Aluminum, Iron, Lead, and Water by the Discrete Ordinates Method , 1994 .

[3]  Y. Harima,et al.  Detailed behavior of exposure buildup factor in stratified shields for plane-normal and point isotropic sources, including the effects of bremsstrahlung and fluorescent radiation , 1993 .

[4]  S. Jiang,et al.  Gamma-Ray Buildup Factors for a Point Isotropic Source in Stratified Spherical Shields , 1989 .

[5]  D. K. Trubey,et al.  Effects of incoherent and coherent scattering on the exposure buildup factors of low-energy gamma rays , 1988 .

[6]  A. Natarajan,et al.  Effect of fluorescence in deep penetration of gamma rays , 1987 .

[7]  Y. Harima,et al.  A comparison of gamma-ray buildup factors for low-Z material and for low energies using discrete ordinates and point Monte Carlo methods , 1987 .

[8]  Shun-ichi Tanaka,et al.  Point Isotropic Buildup Factors of Gamma Rays, Including Bremsstrahlung and Annihilation Radiation for Water, Concrete, Iron, and Lead , 1985 .

[9]  Shun-ichi Tanaka,et al.  Buildup Factors of Gamma Rays Including Bremsstrahlung and Annihilation Radiation for Water, Concrete, Iron, and Lead , 1984 .

[10]  Y. Harima,et al.  An approximation of gamma-ray buildup factors by modified geometrical progression , 1983 .

[11]  D. K. Trubey,et al.  Effect of Fluorescence, Bremsstrahlung, and Annihilation Radiation on the Spectra and Energy Deposition of Gamma Rays in Bulk Media , 1982 .

[12]  G. L. Simmons,et al.  Point Isotropic Gamma-Ray Buildup Factors in Concrete , 1975 .

[13]  Y. Nishiwaki,et al.  An Approximate Transmission Dose Buildup Factor for Stratified Slabs , 1969 .

[14]  D. Broder,et al.  Transmission of gamma radiation through heterogeneous media , 1962 .

[15]  D. K. Trubey,et al.  STRATIFIED SLAB GAMMA-RAY DOSE-RATE BUILDUP FACTORS FOR LEAD AND WATER SHIELDS , 1958 .

[16]  G. L. Simmons,et al.  Photon point source buildup factors for air, water, and iron , 1980 .