Positron-helium collisions: Positronium formation into an arbitrary excitedSstate

The scattering amplitude for positronium formation into arbitrary excited $S$ states in positron-helium collisions in which the residual helium ion is left in the ground state, is obtained in a closed form using the first Born approximation and the first-order exchange approximation. Retaining both the post and the prior forms of the interaction potential, cross sections are computed for several incident positron energies in the range 20-2000 eV. For these energies the asymptotic limit of $n^3$ times the cross section as $n\to \infty$ is attained roughly within 0.1% beyond the excited state $16S$.