FAST SAMPLING ALGORITHM FOR THE SIMULATION OF PHOTON COMPTON SCATTERING

Abstract A simple algorithm for the simulation of Compton interactions of unpolarized photons is described. The energy and direction of the scattered photon, as well as the active atomic electron shell, are sampled from the double-differential cross section obtained by Ribberfors from the relativistic impulse approximation. The algorithm consistently accounts for Doppler broadening and electron binding effects. Simplifications of Ribberfors' formula, required for efficient random sampling, are discussed. The algorithm involves a combination of inverse transform, composition and rejection methods. A parameterization of the Compton profile is proposed from which the simulation of Compton events can be performed analytically in terms of a few parameters that characterize the target atom, namely shell ionization energies, occupation numbers and maximum values of the one-electron Compton profiles.

[1]  P. Pattison,et al.  Multiple scattering and the Compton profile of titanium , 1976 .

[2]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[3]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[4]  B. J. Bloch,et al.  Atomic L -shell Compton profiles and incoherent scattering factors: Theory , 1973 .

[5]  P. Eisenberger,et al.  Compton Scattering of X Rays from Bound Electrons , 1970 .

[6]  Richard B. Firestone,et al.  Table of Isotopes , 1978 .

[7]  R. Ribberfors,et al.  X-ray incoherent scattering total cross sections and energy-absorption cross sections by means of simple calculation routines , 1983 .

[8]  F. Rohrlich,et al.  The Theory of Photons and Electrons , 1956 .

[9]  K Doi,et al.  The validity of Monte Carlo simulation in studies of scattered radiation in diagnostic radiology. , 1983, Physics in medicine and biology.

[10]  F. Cleri.  Low-energy photon scattering simulations with the Monte Carlo code ACCEPT , 1990 .

[11]  W. Nelson,et al.  Monte Carlo Transport of Electrons and Photons , 1988 .

[12]  J. B. Mann,et al.  Hartree-Fock Compton profiles for the elements , 1975 .

[13]  J. Baró,et al.  Analytical cross sections for Monte Carlo simulation of photon transport , 1994 .

[14]  J. H. Hubbell,et al.  Atomic form factors, incoherent scattering functions, and photon scattering cross sections , 1975 .

[15]  Roland Ribberfors,et al.  Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states , 1975 .

[16]  Y. Namito,et al.  Implementation of the Doppler broadening of a Compton-scattered photon into the EGS4 code , 1994 .

[17]  K. Berggren,et al.  Incoherent-x-ray-scattering functions and cross sections ( d σ d Ω ′ ) incoh by means of a pocket calculator , 1982 .

[18]  Martin J. Berger,et al.  Response functions for sodium iodide scintillation detectors , 1972 .