T-matrix theory of positron annihilation onhydrogen

Abstract

The transition amplitude for electron-positron annihilationduring positron-hydrogen scattering is formulated in terms ofthe half-shell T-matrix elements obtained from a solution ofthe momentum space Lippmann-Schwinger equation. The derivedexpression is well defined at energies below the positronium (Ps)formation threshold. However, singularities in the transitionamplitude exist at energies above the Ps-formation threshold.The annihilation parameter for positron-hydrogen scattering iscomputed in a variety of models at energies below thePs-formation threshold. Calculations with the largest basisreproduce previous variational calculations of ZJeff forthe J = 0 and 1 partial waves. Accurate values ofZJeff were also given for the J = 2, 3 and 4 partialwaves to give a summed Zeff that is probably the mostaccurate so far reported.