Threshold behavior of positronium formation in positron-alkali-metal scattering

We consider positron scattering on the alkali-metal atoms of Li, Na, and K at very low energies, where only the elastic scattering and positronium formation in the ground state are the two open channels. Utilizing the recently developed two-center convergent close-coupling method [ Lugovskoy, Kadyrov, Bray and Stelbovics, Phys. Rev. A 82 062708 (2010)] we investigate the behavior of the cross sections as the impact energy goes to zero and demonstrate their convergence. The study sets quantitative benchmarks for any rigorous theoretical treatment of the collision problems