The inclusion of π functions in the treatment of low-energy positron-hydrogen-molecule scattering by a generalisation of the Kohn method

In the application of a generalisation of the Kohn method to low-energy positron-hydrogen-molecule scattering which was described in a recent letter, up to 31 short-range correlation functions, made up of one-particle functions of sigma symmetry, were included in the trial function. In the calculation described in this paper, the flexibility of the trial function is greatly improved by the inclusion of up to 64 short-range correlation functions of which 32 contain products of one-particle functions of pi symmetry. The inclusion of the pi functions has a very big effect on the calculated results, especially at very low energies. The behaviour of the phaseshift values with increasing incident energy is qualitatively similar to the behaviour of the corresponding S-wave phaseshifts in low-energy positron-helium scattering. Comparison with experiment indicates that the results reproduce qualitatively the experimental trend at very low energies but higher partial waves must make a significant contribution to the total cross section above about 0.1 eV. The improved results can be attributed to the much more satisfactory description of the polarisation of the hydrogen molecule made possible by the inclusion of pi functions.