Validity of the Four-Parameter Empirical Formula in Approximating the Response Functions for Gamma-ray, Neutron, and Secondary Gamma-ray Skyshine Analyses

Abstract

A four-parameter approximating formula, R=A e a x b f(x), accurately represents the skyshine line beam response function (LBRF) as a function of the distance (x) of the source-to-detector separation. Here, A is a constant for a given source energy and f(x)=e cx x dx is a damping factor. The four parameters are obtained as follows. 1. The value of parameter a corresponds to that of the LBRF at x=1 meter, which is the result of integrating the basic dose spectrum due to a single scattering particle from an emitted beam for a specified angle and a specified source energy. 2. The value of parameter b corresponds to the slope of a straight line of the response function, log R vs. log x, in the range of small distance from a source, where a single scattering particle dominates. 3. The damping factor (f (x)) represents the attenuation trend of the LBRF at distances far from the source; the values of parameters c and d control the quantity of attenuation. The necessary reference LBRF data for point mono-directional photon source energies ranging from 0.1 to 10MeV were generated using the EGS4 Monte Carlo code at 20 emission angles from 0.0 to 180° for 24 source-detector distances up to 2,000 m. The validity of using the four-parameter formula to interpolate the LBRF in the source-to-detector distance, in the emitted angle, and in the energy was also ascertained. Furthermore, this formula was applied to the skyshine conical beam response function (CBRF) for a neutron and an associated secondary gamma-ray with the source energy ranged from thermal to 3 GeV. It was ascertained that the CBRF could be accurately approximated by an interpolation of the fitting parameters at an arbitrary distance and emitted cosine angle.