A novel approach to improving the calculation of the Compton X-ray scattering cross section.
From the authors' Abstract:
"A review of the Impulse Approximation (IA) for calculating Compton photon scattering probabilities by bound electrons reveals a paucity of measured, double-differential cross-section (DDCS) data with respect to angle and energy, especially for scattered photon with energies near that of the incident
photon energy, E. The K-shell DDCSs derived with IA display undesirable discontinuities and poorly match the available experimental continuous DDCSs between the Compton energy E_f and E. Similar discrepancies with respect to available experimental data are displayed by the S-matrix results. Because
numerical evaluation of IA is neither practical nor straighforward, we have replaced the electron momentum in the energy-momentum conservation with an ad hoc concept of partial electron momentum to show the feasibility of reducing such discrepancies. In the proposed ad hoc DDCS, called here the blended impulse approximation (BIA), this replacement is combined with the incoherent approximation. BIA removes the undesirable discontinuities in the DDCS, provides improved ageement with all existing experimental data, and also provides a general DDCS form for incorporating the evaluated experimental data.
We suggest that the S-matrix energy-momentum conservation could also use the ad hoc concept of partial electron momentum, with benefits similar to those for the IA case. Further developmenot of BIA requires a
measurement of a comprehensive set of DDCS, to help find an adequate set of shell-dependent expressions for the partial electron momentum. In conclusion, we suggest that the concept of partial electron momentum may have a direct physical significance for the photon: the Compton interaction is such that the photon 'sees' only a part of the electron momentum. Alternatively, it might indicate the need for a revised mechanism of the Compton effect that would be different for the free and the bound electrons."
PACS number: 2.80.Cy
Rights:
Open access:
Copyright@2003 by Corneliu I. Costescu, Jeffrey F. Williams and Iwan Kawrakow
