Moments of the generalised oscillator strength distribution and total inelastic x-ray scattering cross sections for He and H-

Abstract

Moments, S( mu ,K), of the generalised oscillator strength distribution are global properties of the Bethe surface. Although S(O,K), S(-1,K) and S( mu ,0) have been thoroughly studied, little is known about the other moments for K not=0. This paper describes high accuracy calculations of S(1,K) and S(2,K) for He and H-. Electron correlation effects are found to be important. A comparison of the theoretical results for helium with experimental ones suggests that there are large errors in the latter. Asymptotic forms that should be useful for more complex systems are presented. The moments are used to calculate total inelastic X-ray scattering cross sections differential with respect to the solid angle by Bonham's new method. The Bonham cross sections differ from the usual Waller-Hartree cross sections at large angles, and the differences increase with the frequency of the incident X-ray. The inelastic cross sections are combined with elastic ones to permit comparison with the total cross sections for scattering of 6 keV photons from helium measured by Ice et al. (1978) with synchrotron radiation. The calculations which include Bonham inelastic cross sections are in better agreement with experiment than the Waller-Hartree results. However, higher accuracy experiments are needed to definitively exclude the Waller-Hartree cross sections.