T-matrix theory of positron annihilation on hydrogen

The transition amplitude for electron-positron annihilation during positron-hydrogen scattering is formulated in terms of the half-shell T-matrix elements obtained from a solution of the momentum space Lippmann-Schwinger equation. The derived expression is well defined at energies below the positronium (Ps) formation threshold. However, singularities in the transition amplitude exist at energies above the Ps-formation threshold. The annihilation parameter for positron-hydrogen scattering is computed in a variety of models at energies below the Ps-formation threshold. Calculations with the largest basis reproduce previous variational calculations of Z_eff^J for the J = 0 and 1 partial waves. Accurate values of Z_eff^J were also given for the J = 2, 3 and 4 partial waves to give a summed Z_eff that is probably the most accurate so far reported.