Application of a generalisation of the Kohn variational method to the calculation of cross sections for low-energy positron-hydrogen-molecule scattering

The phaseshift corresponding to the lowest partial wave and the associated approximation to the total cross section are calculated for low-energy positron-hydrogen-molecule scattering using a generalisation of the Kohn variational method. The trial wavefunction is expressed in terms of confocal elliptical coordinates and is a generalisation of the wavefunction used by Massey and Ridley (1956) in their treatment of low-energy electron-hydrogen-molecule scattering. The most accurate target wavefunction used takes into account 50% of the electronic correlation energy. Up to 31 short-range correlation functions, made up of products of one-particle functions of sigma symmetry, are included in the trial wavefunction. Except at incident positron energies below about 2 eV, reasonable agreement with experiment is obtained below the positronium formation threshold at 8.63 eV.