On Energy Matrices for the Independent Particle Model

Abstract

A method which makes use of Fourier transforms of two-body interactions for the calculations of energy matrices in the independent particle model is proposed. The non-central interactions as well as central ones can be easily expanded into series of tensor products of spherical harmonics by this procedure. Furthermore, the radial integrals can be reduced to simple integrals which involve the Fourier transforms of the radial dependence of the interactions. For the harmonic oscillator wave functions, the procedure can be easily carried out and explicit formulas for the integrals are obtained. Useful tables for the calculations of the integrals for the central, tensor and spin-orbit interactions are given.