Positron-atom scattering using a modified Kohn variational technique

Abstract

An analysis of the zero-energy positron-hydrogen and positron-helium systems using various approximations to the target ground-state wavefunction is presented. A modification of the normal Kohn variational method is used in which a quantity, aQ, which becomes the Kohn scattering length if the target wavefunction is exact, is related to the trial wavefunction Psi t through an integral expression. By comparing the results obtained with the definitive values for the positron-hydrogen system, it is conjectured that if the values of aQ display a local minimum when all the nonlinear parameters of Psi t are varied, then this local minimum of aQ is an upper bound on the exact scattering length. Using this criterion to analyse the positron-helium results, it is concluded that this method may be considered as an alternative to the 'method of models' procedure, since both methods give similar results.