Anomalous Dispersion and Scattering of X-Rays

Abstract

The theoretical expressions for the anomalous dispersion of x-rays have been integrated for any positive value of ${p}_{q}$ in a ${C}_{q}{\ensuremath{\lambda}}^{{p}_{q}}$ term in the distribution of "dispersion" oscillators for the $q$ shell of electrons. This distribution may be written generally as the sum of $n$ terms of the form ${C}_{\mathrm{qn}}{\ensuremath{\lambda}}^{{p}_{\mathrm{qn}}}$ or, as is commonly done, as a single term. Damping has been retained, its effect evaluated and shown to be negligible except for $\ensuremath{\lambda}$ extremely close to the wavelength of an absorption discontinuity. With damping neglected, universal dispersion curves are presented. If ${p}_{q}$ and ${g}_{q}$ (the oscillator strength) are known, the anomalous part of the refractive index or of the atomic scattering factor can be readily deduced from the universal curves.Comparison of the more exact theoretical values with experiment shows less satisfactory agreement than before.