Anomalous Dispersion and Scattering of X-Rays

The theoretical expressions for the anomalous dispersion of x-rays have been integrated for any positive value of $p_q$ in a $C_q{\lambda }^{p_q}$ 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 $C_{\mathrm{qn}}{\lambda }^{p_{\mathrm{qn}}}$ or, as is commonly done, as a single term. Damping has been retained, its effect evaluated and shown to be negligible except for $\lambda$ 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.