Correlation and X-ray scattering. I. Density matrix formulation

Abstract

Equations suitable for obtaining values of the coherent and total intensities of X-ray radiation scattered by N-electron atomic systems are developed from the 1- and 2-particle density matrices. Although electron scattering within the first Born approximation can be treated in the same fashion, a separate consideration of this problem is not required since the scattered electron and X-ray intensities are related by equations well established in the literature. The general formalism presented here is such that it easily allows the computation of X-ray scattering factors and intensities to extend beyond the Hartree–Fock approximation, thereby incorporating electron correlation effects. Evaluation of the relevant equations requires the natural orbitals or the natural spin orbitals and the natural geminals or the natural spin geminals. These can always be obtained from the 1- and 2-particle density matrix analyses of the N-electron wavefunction Ψg characterizing the atomic state. In the event that Ψg is approximated by a single Slater determinant, the equation for the total scattered X-ray intensity reduces to the familiar Waller–Hartree result.