Evaluation of the matrix element for positron impact ionization of atomic hydrogen near threshold in the effective charge model

The evaluation of the matrix element for positron impact ionization of atomic hydrogen near threshold in the effective charge model wherein the final state is a product of two Coulomb functions - one for the attractive electron-proton and the other for the repulsive positron-proton interaction. Since the normalization factor of the part of the wave function corresponding to the repulsive interaction vanishes exponentially at threshold, it was thought up till now that the matrix element would be almost insignificant over a considerable portion of the energy interval near the threshold. The effect of this exponentially vanishing normalization factor is appropriately compensated for. To illustrate the striking contrast of our new finding with the earlier view we have calculated the total cross section for the 'no-screening' case where we get a square threshold law against the exponentially vanishing result of Geltman. (author). 12 refs