On the semi-classical description of molecular orbiting collisions

The semi-classical analysis of molecular orbiting collisions is discussed in the context of Breit-Wigner theory. The explicit introduction of a complex energy is used to characterize the quasi-stationary states in the dip of the effective potential characterizing the collision. Expressions for the resonance energies and widths of the quasi-stationary states are derived from the semi-classical wavefunctions and a formula given for the resonant contribution to the measurable total elastic cross section. The semi-classical wavefunctions are derived with the help of connection formulae based on an exact solution of the Schrödinger equation for a parabolic well and a parabolic barrier. The connection formulae for the case a parabolic well are derived and their properties developed.