Positronium formation in highly excited states ine+-Li collisions

The cross sections—differential and integral—for electron capture by positrons from atomic lithium forming positronium in highly excited $\mathrm{ns}$ states are calculated by the use of the first Born approximation at several incident energies. In addition to the effect of the valence electron, the effect of the core term is taken into account explicitly. A straightforward technique is suggested for the evaluation of the transition amplitudes, the attractive part of which is given in a closed form, while the repulsive part involves a single-dimensional integral that is evaluated numerically. The asymptotic nature of the Ps formation as $n\to \infty$ is also discussed. It is seen that the asymptotic Ps-formation cross section obeys an inverse $n^3$ law irrespective of the energy. The angular distribution shows a zero depending on the projectile energies but almost independent of the principal quantum number $n$. The reported results for Ps formation for $2\le n\le \infty$ are quite new.