Positron scattering by equivalent one-electron models ofhelium

Abstract

Low-energy positron-helium scattering is investigated usingthree different one-electron models of helium in order to findout if such a model is capable of yielding accurate results forelastic scattering, positronium formation and positron-electronannihilation. Comparisons are made with the accurate resultsobtained from ab initio variational calculations of VanReeth 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 heregives accurate values for the elastic scattering phase shiftsthroughout most of the energy range up to the positroniumformation threshold. However, near-threshold resonancesassociated with this model have substantial effects on all thepartial wave contributions to the positronium formation crosssection that have been investigated. The other two helium modelsyield rather less accurate elastic scattering phase shifts butthe positronium formation cross sections are in goodqualitative, and even reasonably good quantitative, agreementwith the accurate results. None of the models yields veryaccurate results for the annihilation cross section.