Rotation—Electronic Interaction in the Rydberg States of Diatomic Molecules

Abstract

The theoretical foundation of Hund's coupling cases for the interaction between rotation and electronic motion is re-examined. The relationship between different cases is shown by angular-momentum coupling techniques. Rotational interaction terms neglected in the Born—Oppenheimer adiabatic type approximation and in the idealized Hund's cases are considered in particular. For application to Rydberg states, new and improved perturbed energy expressions of Λ doubling for spectroscopic use are derived up to the fourth order for a near Hund's Case b′ diatomic molecule and up to the second order for a near Hund's Case d′ diatomic molecule. Specific formulas are given for the p-term (L=1) and the d-term (L=2) complexes. For the approach towards cases intermediate between b′ and d′, secular determinants for this perturbation problem are formulated starting both from ideal case b′ and from ideal case d′ using two parameters, instead of one, for the d-term complex. These two approaches are shown to give equivalent results proving the consistency of the perturbations and assumptions used at both ends. The nature of these assumptions as well as the physical basis for the transition between Case b′ and Case d′ are shown.