ANALYTICAL CROSS-SECTIONS FOR MONTE-CARLO SIMULATION OF PHOTON TRANSPORT

Simple analytical approximations to the photon-interaction cross sections in the energy range from 1 keV up to approximately 1 GeV are proposed. The analytical formulae are obtained as combinations of familiar approximations and numerical fits. Differential cross sections for coherent and incoherent scattering are given in terms of new analytical approximations to the atomic form factor and the incoherent scattering function. Pair production is described by means of the Bethe-Heitler differential cross section for exponential screening, together with both a Coulomb correction and an empirical low-energy correction. The calculation of partial attenuation coefficients for these interactions requires only a single numerical quadrature. Simple analytical algorithms for random sampling from the proposed differential cross sections are described. A new parametrization of the photoelectric cross section is also given. The resulting total attenuation coefficients agree with recent compilations to within approximately 0.5%. The parametric tables included in this paper contain all the information required for Monte Carlo simulation, as well as for the evaluation of attenuation coefficients, for elements with Z = 1 to 92 and photon energies down to either the L1 edge or 1 keV, whichever is the largest.