Positron scattering by equivalent one-electron models of helium

Low-energy positron-helium scattering is investigated using three different one-electron models of helium in order to find out if such a model is capable of yielding accurate results for elastic scattering, positronium formation and positron-electron annihilation. Comparisons are made with the accurate results obtained from ab initio variational calculations of Van Reeth and Humberston (Van Reeth P and Humberston J W 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3651). The most elaborate helium model used here gives accurate values for the elastic scattering phase shifts throughout most of the energy range up to the positronium formation threshold. However, near-threshold resonances associated with this model have substantial effects on all the partial wave contributions to the positronium formation cross section that have been investigated. The other two helium models yield rather less accurate elastic scattering phase shifts but the positronium formation cross sections are in good qualitative, and even reasonably good quantitative, agreement with the accurate results. None of the models yields very accurate results for the annihilation cross section. (author)