Hylleraas Method for Many-Electron Atoms.II.Integrals Over Wave Functions With One Interelectronic Coordinate

摘要

A procedure is proposed to evaluate matrix elements containing r_(ij)~v linked with angular functions.Using this procedure,the different types of two-,three-,and four-electron radial and angular integrals that appear in a five-electron atom,in the case of only one r_(ij) coordinate per basis function,are written in a compact form,separated in radial coordinates of one electron.The general formulas with which to obtain the integrals for powers v >= 1 are developed,based on the orthogonality of the Legendre polynomials.