Incoherent x-ray scattering factors calculated from impulse-approximation Compton profiles: A comparison with the Waller-Hartree theory

Incoherent x-ray scattering factors have been calculated for Li through Ne by integrating over Compton profiles calculated using the impulse approximation. Analytic expressions for the impulse-approximation Compton profiles (IACP) were derived from Clementi-Hartree-Fock (HF) analytic wave functions. Both experimental and theoretical HF electron binding energies were used in the numerical computation of the IACP inelastic scattering factors. These IACP scattering factors are compared with results obtained from the Waller-Hartree (WH) theory using HF atomic wave functions and a configuration-interaction (CI) wave function. Differences of as much as a factor of 2 are found at low scattering angles between the IACP and WH results calculated from HF wave functions. At low scattering angles the IACP results are in closer agreement with WH scattering factors calculated from the CI wave function than those computed from HF functions. A realistic possibility for obtaining more accurate inelastic scattering factors is demonstrated by direct integration over Compton profiles than can be computed from the WH scheme.