A scattering theory of diatomic molecules

We present a unified theory of diatomic molecules which reconciles bound state spectroscopy and atomic scattering theory. The total wave-function is expanded in a complete set of atomic channel states which is entirely equivalent to an expansion in Hund's case (e) electronic-rotational states. An analysis of the coupled radial, that is vibrational, functions places strong constraints on the asymptotic properties of the molecular wave-functions. These are presented in terms of the reactance K and scattering S matrices of atomic scattering theory which offers a uniform treatment for open channels (inelastic scattering and continuum spectroscopy), closed channels (bound state spectroscopy) and mixtures of both (predissociation). The normalization of the total wavefunction is derived and related to the asymptotic boundary conditions both for continuum and bound states.