Analytic Expressions for the One‐Center Elements of Compton Profiles. Slater‐Type Orbitals

Abstract

Analytic Expressions for the One-Center Elements of Compton Profiles. Slater-Type 0 rbitals R. RAMfREZ2) and M. C. B O W BY The momentum distribution of electrons in atoms, molecules, and solids has been studied in the past years by inelastic Compton scattering with monochromatic X and r-ray radiation /1, 2/. Within the impulse approximation (IA) /3, 4/ the shape of the Compton line can be related to the directional Compton profile (DCP) . The IA is based on the following approximations: i) scattering of single, independent electrons; ii) neglect of the electron binding energy;iii) plane-wave description of the final electron state. In this framework the DCP, JDCP( <), can be written a s where q(px, p , pz) is the single-particle density matrix of the Fermion system in momentum space. q ( p order density matrix r(r, r') /5/ by double Fourier transformation:

Accurate atomic momentum integrals and Compton profiles

“…Consequently several theoretical contributions to the study of atomic electron momentum distributions have been reported so far, including analytical expressions for electron momentum distributions of small atoms using Slater basis sets [13][14][15][16][17], as well as calculations of CP of elements at Hartree-Fock level (HF) using double-zeta and numerical wave functions [18,19]. Furthermore, total momentum expectation values and other p-space properties [20][21][22] have been computed, and more recently, Ozdogan and Eraslam have published analytical calculations of CP using Clementi Roothan-Hartree-Fock functions for atoms ranging from helium to neon [23].…”