Optical model theory for positron annihilation during scattering

The possibility of the annihilation process occurring during scattering of a positron by an atomic target is taken into account by means of an absorption potential. The imaginary absorption potential is chosen so that its matrix element in the plane wave Born approximation correctly reproduces existing perturbation theory expressions for the annihilation cross section. The momentum space Lippmann-Schwinger equations for positron-hydrogen scattering with the imaginary absorption potential are solved for some simple close-coupling expansions at energies below the positronium formation threshold. The optical potential calculations agree with previous perturbation theory calculations