Parameter search of geometric-progression formula for gamma-ray isotropic point source buildup factors up to depths of 100 mfp, including contribution of secondary radiations

Abstract

The form of K(E,X) in the Geometrical Progression (G-P) fitting function for 28 single-material gamma-ray buildup factors was improved to accurately approximate for deep penetration up to 100 mean free paths (mfp). The reference data were generated with Invariant Embedding (IE method) code treated Klein-Nishina scattering cross section accurately, included all secondary radiations of fluorescence and bremsstrahlung, and covered the energy range 0.015-15 MeV and up to 100 mfp. The search procedure of fitting parameters to gamma-ray buildup factors was revised from the least squares fit (LSF) to the minimization of maximum fractional deviation (MMD). Revised K(E,X) has 7 parameters. Here two values of Xk and Xm parameters were fixed, and the remainder parameters were determined using the (MMD). For an energy not listed in the reference, the values of G-P fitting parameters were determined using the interpolation method of Akima. By the same method the values of G-P fitting parameters for equivalent atomic number of a compound or a mixture were determined. The maximum errors of the present fitting parameters within 40 mfp were almost the same values to the ANSI/ANS-1991 or below. Those above 40 mfp were almost the same values within 40 mfp, or a little large.