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

Calculation of Gamma-Ray Buildup Factors up to Depths of 100 mfp by the Method of Invariant Embedding. (I). Analysis of Accuracy and Comparison with Other Data.

“…Although it was reported by Hirayama and Trubey, 13) Kistos et al 7) and Chibani 10) that effects of coherent and incoherent scattering on buildup factors at low energy are substantial, the buildup factors to be generated in the present work is based on the Compton scattering of gamma-ray with the freeelectron. The buildup factor computed with coherent and incoherent scattering should be used combined with the mass attenuation coefficient including both coherent and incoherent scattering cross sections.…”

“…It is confirmed numerically that the error due to the angular mesh associated with the transport calculation with 13 angular divisions is less than 10% up to depths of 100 mfp. Kistos et al 7) reported that an extremely fine angular mesh was required in their calculations of exposure buildup factors by the SN1D code. The error due to angular mesh was estimated 2% at depth of 30 mfp, when S 64 Gaussian quadrature was applied.…”

“…The EGS4 data agree well with the ANS data except for iron at 10 MeV and for lead at 0.1 MeV and 10 MeV, where some discrepancies are found. Kistos et al 7) calculated the exposure buildup factors for some materials up to depths 30 mfp by using the SN1D code based on the discrete ordinates method. Their work aims at taking into account the effect of incoherent and coherent scatterings.…”

Time-Dependent Neutron and Photon Dose-Field Analysis

“…Both discrete-ordinates and Monte-Carlo methods have been used in buildup factor studies by Hirayama, Harima and others [27] in which the effects of secondary photons from bremsstrahlung and fluorescence were identified. Hirayama [28], using plane geometry and Monte Carlo, and Kitsos [29], who used spherical geometry and discrete-ordinates, both demonstrated that the inclusion of incoherent and coherent scattering phenomena in cross sections tends to increase exposure buildup at energies above 10 keV. Kitsos later showed that by including photons from bremsstrahlung and fluorescence, exposure buildup factors increase significantly [30].…”

Calculation of Gamma-Ray Buildup Factors up to Depths of 100 mfp by the Method of Invariant Embedding, (I)

“…Kistos et al 7) calculated the exposure buildup factors for some materials up to depths 30 mfp by using the SN1D code based on the discrete ordinates method. Their work aims at taking into account the effect of incoherent and coherent scatterings.…”