An approximate treatment of shape resonances in elastic scattering

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Abstract
New connection formulae for barrier penetration problems are derived based on the analytic solution of an inverted Morse potential. These are employed to determine approximate phase shifts for atom-atom collisions and in particular the positions and widths of the quasibound states of the effective potential controlling the collisions. Good agreement with the results derived using connection formulae based on a parabolic barrier is obtained. A complex angular momentum treatment of the resonances due to these quasibound states is discussed. Some comparisons with exact calculations are presented and a first-order treatment is shown to be very accurate.