RKR-type inversion of the diatomic energy shifts due to breakdown of the Born–Oppenheimer approximation

Abstract

The principal effects of the breakdown of the Born–Oppenheimer approximation on the vibration–rotation energies of a diatomic molecule can be represented by the expectation values of terms to order (me/Mi) in the effective Hamiltonian, where me is the electron mass and Mi is the mass of atom i. This paper examines the possibility of inverting these expectation values to obtain the correction functions as functions of the internuclear distance r, using a generalization of the semiclassical Rydberg–Klein–Rees method. It is shown that the correction functions are not completely determinable from the inversion, and the form of the determinable combinations is obtained.Key words: diatomic molecules, vibration–rotation energies, isotope effects, Born–Oppenheimer breakdown, Rydberg–Klein–Rees method.