Reduction of semiclassical phase shifts for potential scattering to resonance form

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Abstract
The semiclassical theory of shape or orbiting resonances is discussed within the context of the Jost function approach to potential scattering. The S matrix is considered as a function of four variables : energy, angular momentum, potential coupling constant and mass, each of which is allowed to take complex values. A semiclassical quantization condition is obtained which determines the poles of the S matrix. For a sharp resonance, the S matrix reduces to a Breit-Wigner form and it is shown that the use of these four variables provides an equivalent description of a resonance in this case. In addition the semiclassical analysis of the three-turning-point problem is extended to that of five turning points. The five-turning point case occurs in the elastic scattering of reactive systems and in the scattering of excited states of diatomic systems.