Distorted waves with exact nonlocal exchange: A canonical function approach

Abstract

The Canonical Function Method (CFM) is developed and applied, for the first time, to the distorted wave problem with exact nonlocal exchange. In electron impact ionization of hydrogenic systems, the latter originates from the Pauli exclusion principle that leads, in the Hartree–Fock approximation, to a radial Schrodinger equation of an integro-differential type. The application of the CFM with static and polarization potentials allows us to obtain the phaseshifts and scattering lengths in the s-wave singlet and triplet states at high (≥5 eV) and low energies (≤0.1 eV). The results are compared with those obtained by other methods based on exact exchange, local equivalent-exchange potentials and recently developed spectral integral equation methods (S-IEM). The accuracy, stability, and speed of convergence of the CFM are analysed and compare favorably with other methods including the highly accurate S-IEM. At very low energies, the CFM is superior to all known methods.PACS Nos.: 34.00.00, 34.50.–s, 03.65.–w, 02.60.Nm, 02.60.–x