Complex-Angular-Momentum Analysis of Atom-Atom Scattering Experiments

$S$-matrix elements typically encountered in atom-atom scattering may be phenomenologically parametrized using meromorphic functions of complex angular momenta. The contribution to the scattering amplitude of each pole of the $S$ matrix is of such a simple nature (effectively, decaying oscillations for parameters encountered in practice) as to greatly facilitate the deduction of the phase shifts from scattering data. Some of these poles should be close to the true (Regge) poles of the exact $S$ matrix about which much theoretical information is available. There is some discussion outlining how many diverse phenomena such as rainbows, orbiting, and curve crossing can all be parametrized under the same scheme, thus leading to their unified treatment.