Positronium formation by electron capture from hydrogen-like ions

Two different impulse approximations are provided for the problem of fast positron collisions with hydrogen-like ions. One of the impulse approximations is formulated by making a consistent expansion of the scattering wave function in powers of the weak interaction to the strong. The other impulse approximation is formulated by making a consistent expansion of theT-matrix in powers of the weak interaction to the strong. In this impulse approximation, the opposite limits of the target nuclear charge tending to zero and to infinity are examined. Differential and angle-integrated cross sections are computed for ground-state positronium formation from hydrogen within the impulse approximations. The full peaking approximation is employed in the evaluation of theT-matrix. By 300 eV, the impulse approximations for the angle-integrated cross section are in close agreement with the strong potential Born and the exact second Born calculations.