Nonrelativistic quantum theory of the contact inelastic scattering of an x-ray photon by an atom

Abstract

The nonrelativistic analytical structure of the doubly differential cross section of the contact inelastic scattering of an x-ray photon by a free atom is determined by means of the irreducible tensor operator theory outside the frame of the impulse approximation. For the neon atom in the vicinity of the 1$s$ shell ionization threshold our theory predicts the existence of the distinct fine structure of the cross section caused by transitions of the atomic core electrons into the excited discrete spectrum states. The results of our calculations with inclusion of the effects of radial relaxation, inelastic scattering through the intermediate states, and elastic Rayleigh scattering, are predictions, while at the $22\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ incident photons they compare well with the synchrotron experiment by Jung et al. [Phys. Rev. Lett. 81, 1596 (1998)].