Abstract
A simple equation is derived from one- and two-particle density matrices in the free-Fermi-gas approximation for obtaining the incoherent intensity of X-rays scattered by an atomic N-electron system. The accuracy of the equation is tested on the Thomas-Fermi-Dirac statistical atomic model. The numerical results are compared with those obtained from the known Heisenberg-Bewilogua function and with the atomic incoherent intensities calculated by D. T. Cromer [J. Chem. Phys. (1967). 47, 1892-1893; (1969). 50, 4857-4859] using complete Waller-Hartree theory and the HF SCF model. The results obtained by the present method from the TFD model are in good agreement with Cromer's data.
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