An examination and assessment of available incoherent scattering s-matrix theory, also compton profile information, and their impact on photon attenuation coefficient compilations

Abstract

The Klein-Nishina formulae for the differential and integral cross sections for Compton (or incoherent) scattering of x-ray photons from atomic electrons assume that the electrons are free (unbound) and at rest, which is a good approximation for photons of the order of 1 MeV or higher, particularly for low-Z target materials. The probability for dislodging bound electrons can be taken into account at least approximately by including an incoherent scattering function S(x,Z) in the differential Klein-Nishina formula. Currently available systematic theoretical tabulations of S(x,Z), where x is a momentum transfer variable dependent on the photon deflection angle and the photon incident energy do not use S-matrix theory with its claimed higher accuracy. The currently most widely-used S(x,Z) tables are non-relativistic. Recently (1998) Kahane has used the Ribberfors-Berggren relativistic treatment to compute systematic tables of S(x,Z). These new values of S(x,Z)have not yet been exploited for computing relativistic bound-electron incoherent scattering integrated cross sections a^, nor for triplet (pair production in the field of the atomic electrons) cross sections K e which also require S(x,Z) for their computation. The motion of the atomic electrons around the atomic nucleus gives rise to a Doppler broadening of the apparent energy of the incident photon, resulting in a corresponding broadening of the Compton "modified line" for a given deflection angle of the outgoing scattered photon. The shape of this broadened line is called the "Compton profile." One task of this report is to examine the usefulness and advantages, if any, of S-matrix theory in providing significantly more accurate values of photon interaction cross sections and attenuation coefficients. The other task of this report is to examine the available Compton profile literature and to explore what, if any, effect our knowledge of this line-broadening has on theoretical computations of photon incoherent scattering cross sections and total mass attenuation coefficients.