Numerical determination of elastic positron- and electron-atom scattering phaseshifts

Numerical investigations of both the positron- and electron-hydrogen systems in the elastic scattering energy region are presented. For the positron-hydrogen system, modifications of the Kohn variational method are used in which the quantities etasub(v) and etasub(Q) are related to the trial wavefunction PSIsub(t) through integral expressions using approximations to the target wavefunction psi. The quantities etasub(v) and etasub(Q) become the Kohn elastic phaseshifts when the exact target wavefunction is used. From the results obtained for the positron-hydrogen system it is conjectured that if the values of either etasub(v) or etasub(Q) display a local maximum when all the nonlinear parameters of PSIsub(t) are varied, then this local maximum value is a good approximation to the Kohn elastic phaseshifts that would be obtained by replacing the approximate psi with the exact psi in the particular PSIsub(t) used in the calculations. Application of this procedure to the positron-helium elastic scattering system is given using Hylleraas-type approximations to the helium ground-state wavefunction. Both the positron- and electron-hydrogen systems are analysed in the elastic scattering energy region using a modified optical potential method. The results suggest that the local maximum value of the modified optical potential phaseshift when all the nonlinear parameters of PSIsub(t) are varied, is reasonably close to the normal optical potential phaseshift obtained when the exact psi is used. (author)