An Improved Approximation Formula of Gamma-Ray Buildup Factors for a Point Isotropic Source in Two-Layer Shields

Abstract

An approximation formula of buildup factor for two-layer shields proposed previously was improved to fitting to the newly calculated buildup factors for point isotropic source gamma-rays of 0.1, 0.3, 0.6, 1,3,6 and 10 MeV penetrating two-layer shields combinations of water, iron or lead materials with the Monte Carlo code EGS4 included the effects of Bremsstrahlung and fluorescent radiations. A f-function in the formula was modified to reproduce precisely the reference data up to the total thickness 40 mfp and the value of buildup factor at the interface of two-layer shields. The functions α and β used in improved f-function f(x1,x2) = α(x1)/{α(x1)+B2(x1)*β(x1,x2)x2} were represented by simple formula fitted to reference data in excellent agreement. Consequently, the two-layer shields buildup factor for any arbitrary thickness of the first-layer x1, and the second-layer x2, and for arbitrary source energy can easily be estimated by interpolation of functions α and β with respect to energy.