X-ray scattering in the resonance region: Atomic hydrogen

An approximate theory for the scattering of X-rays by free atoms in the res onance region for both elastic and inelastic scattering is developed based on the exact results through first order in perturbation theory of non rela tivistic X-ray scattering obtained by Gavrila and Costescu [Phys. Rev. A 2, 1752 (1970)]. The A . p corrections for the elastic scattering of X-rays f rom the ground state of atomic hydrogen are evaluated numerically in the re sonance region and the results are compared with the predictions of the opt ical theorem and a dispersion relation using the exact results for the phot o absorption spectrum. The possibility of carrying out a polarization depen dent experiment to observe the contribution to the A . p correction from no n dipole excitations is analyzed and predicted to be feasible with currentl y available X-ray sources.