Variational calculations of the positron-helium scattering length using approximate target wavefunctions

Abstract

Recently Peterkop and Rabik (see abstr. A2987 of 1972) have calculated the positron hydrogen scattering length using an inexact target wavefunction in Kohn's variational method. They showed that the usual minimum principle is violated. Kohn's variational approximation to the scattering length is derived when the trial function includes an approximation to the target wavefunction. In addition calculations are reported of the positron helium scattering length in which several different approximations to the helium ground state wavefunction have been used. The results of Peterkop and Rabik are confirmed and reference is made to the 'method of models' which recovers the minimum principle of Kohn's variational method. A suggestion for extending this method to electron helium collisions is included.