Compton scattering beyond the impulse approximation: Application to the core electrons of carbon

The Compton profile produced by the 1s electrons of carbon has been calculated using (i) the impulse approximation, (ii) the hydrogenic approximation, and (iii) a type of Hartree-Fock self-consistent-field (HF-SCF) approximation. Significant deviations between the hydrogenic and the impulse results are found for incident photon energies below 25 keV. Between the hydrogenic and the quasi-HF-SCF results, the main difference is that the Compton defect and the maximum of the profile are much smaller when using the latter approximation. These differences are discussed in terms of simple models.