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 elem ents obtained from a solution of the momentum space Lippmann-Schwinger equa tion. The derived expression is well defined at energies below the positron ium (Ps) formation threshold. However, singularities in the transition ampl itude exist at energies above the Ps-formation threshold. The annihilation parameter for positron-hydrogen scattering is computed in a variety of mode ls at energies below the Ps-formation threshold. Calculations with the larg est 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.