X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92

Abstract

The primary interactions of low-energy x-rays within condensed matter, viz. photoabsorption and coherent scattering, have been described for photon energies outside the absorption threshold regions by using atomic scattering factors. The atomic scattering factors may be accurately determined from the atomic photoabsorption cross sections using modified Kramers-Kronig dispersion relations. From a synthesis of the currently available experimental data and recent theoretical calculations for photoabsorption, the angle-independent, forward-scattering components of the atomic scattering factors have been thus semiempirically determined and tabulated here for 92 elements and for the region 50-30,000 eV. Atomic scattering factors for all angles of coherent scattering and at the higher photon energies are obtained from these tabulated forward-scattering values by adding a simple angle-dependent form-factor correction. The incoherent scattering contributions that become significant for the light elements at the higher photon energies are similarly determined. The basic x-ray interaction relations that are used in applied x-ray physics are presented here in terms of the atomic scattering factors. The bulk optical constants are also related to the atomic scattering factors. These atomic and optical relations are applied to the detailed calculation of the reflectivity characteristics of a series of practical x-ray mirror, multilayer, and crystal monochromators. Comparisons of the results of this semiempirical, "atomic-like" description of x-ray interactions for the low-energy region with those of experiment and ab initio theory are presented.