An improved approximation formula of gamma-ray buildup factors for a point isotropic source in two-layer shields

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. (author)