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 capa ble of yielding accurate results for elastic scattering, positronium format ion and positron-electron annihilation. Comparisons are made with the accur ate results obtained from ab initio variational calculations of Van Reeth a nd Humberston (Van Reeth P and Humberston J W 1999 J. Phys. B: At. Mel. Opt . Phys. 32 3651). The most elaborate helium model used here gives accurate values for the elastic scattering phase shifts throughout most of the energ y range up to the positronium formation threshold. However, near-threshold resonances associated with this model have substantial effects on all the p artial wave contributions to the positronium formation cross section that h ave been investigated. The other two helium models yield rather less accura te elastic scattering phase shifts but the positronium formation cross sect ions are in good qualitative, and even reasonably good quantitative, agreem ent with the accurate results. None of the models yields very accurate resu lts for the annihilation cross section.