Energies and widths of quasibound levels (orbiting resonances) for spherical potentials

Abstract

Various methods for calculating the energies and widths of quasibound levels (orbiting or shape resonances) for spherical potentials are critically compared. A derivation for the previously-proposed Airy function boundary condition method is presented, and a Weber function boundary condition method for locating resonances which lie above the potential barrier maximum is derived, tested, and found wanting. It is shown that the Weyl m-function method of Hehenberger et al. [J. Chem. Phys. 65, 4559 (1976)] yields results in essentially exact agreement with the time-delay maximum method of Le Roy and Bernstein [J. Chem. Phys. 54, 5114 (1971)]. An improved semiclassical method of calculating these resonance widths, suggested by M.S.Child, is presented and shown to be reliable even for levels lying right at a potential barrier maximum.