The Uncoupled Phase Method for Interactions with Hard Cores

A system of $n$ strongly coupled, two-body channels may be sufficient to describe a given set of reactions. A theoretical calculation on the other hand, might completely neglect one of these channels. The uncoupled phase method (developed by Ross and Shaw) is a nonperturbative formalism (based on a potential model) relating the "uncoupled" scattering amplitudes describing the $n-1\mathrm{}$ channels to the actual amplitudes for all $n$ channels. We demonstrate in this paper that the uncoupled phase method remains a quantitative procedure over a wider range of conditions than originally anticipated. The method is derived for interactions with hard cores. By performing a two-channel computer experiment, the method is seen to be quantitatively accurate for Yukawa interactions with hard cores; this holds for $p$-wave as well as $s$-wave orbital angular momenta, and in the case that one of the channels is closed as well as when both are open.