Measurement of the Atomic Scattering Factor of Ne, Ar, Kr, and Xe

Abstract

To test the accuracy of the Hartree-Fock (HF) method and the reliability of x-ray measurements of the atomic scattering factor $f$, we have determined the scattering of Mo $K\alpha$ radiation by Ne, Ar, Kr, and Xe gases. Values of $f$ were obtained on an absolute basis with an accuracy of about ¼%. Results at small angle yield the mean-square radius of the electron cloud ${〈r^2〉}_{\mathrm{av}}$ and the dispersion correction. For Ne, Ar, and Kr, the values of ${〈r^2〉}_{\mathrm{av}}$ are in good agreement with HF calculations. For Xe, the experimental value is significantly lower. Susceptibility results yield about 6% lower values in each case. Our derived values of the dispersion correction are each more negative than those obtained from published absorption coefficients. At higher angles, our $f$ values differ by less than 0.2 electron unit from the HF values for all the gases; even for Xe the approximate HF values presently available are more nearly accurate than the Thomas-Fermi-Dirac (TFD) values. We conclude that a 4% discrepancy between theory and experiment found by Batterman, Chipman, and DeMarco for metal powders arose from solid-state effects or from difficulties in sample preparation.