Effective range analysis of positron-hydrogen collisions

Humberston [Can. J. Phys. 60, 591 (1982)], using the Kohn variational method, showed that the range of validity of Wigner’s threshold law for positronium formation in positron-hydrogen collisions is extremely narrow for the S wave. To examine the near-threshold behavior, we analyzed ab initio calculations using the multichannel effective range theory of Watanabe and Greene [Phys. Rev. A 22, 158 (1980)] and the single-channel effective range theory of Fabrikant [Opt. Spectrose 53, 131 (1982)] for the positronium-proton channel. We confirmed the presence of a Ramsauer minimum in the L=0 elastic cross section for positronium-proton scattering, and found a similar minimum for L=1. The near-threshold structure is interpreted in terms of a virtual state, resonances, tunneling through and transmission over a barrier, and quantum suppression.