Calculation of The Direct Potential in Electron-Helium Scattering Using Non-Orthogonal Laguerre L2 Basis

Abstract

In this paper first we consider a helium atom in LS coupling configuration. We use a product of a radial function, a spherical harmonic and a spin function as a single-electron orbital function, which are used to build the two-electron basis. The radial function of the single-particle functions are of the non-orthogonal Laguerre basis [1] ()()()(rLrrrlmlmλλλφ1212/exp++−= ) ) , (1) where the are the associated Laguerre polynomials, and m ranges from 1 to the basis size N. The two-electron functions is then written in terms of the product of these orbitals for coordinates r(rLlmλ12+(12nC1 and r2. Here the configuration interaction coefficients ) satisfy the symmetry property ()()()2112211nslllnCC−−+−=, (2) to ensure antisymmetry of the two-electron system states.