Vibrational Transition Probabilities of Diatomic Molecules: I

Abstract

An approximation is made which allows analytic integration of the `overlap', and other, integrals of vibrational wave functions in Morse potentials that arise in the study of the electronic spectra of diatomic molecules. The heavy and lengthy work that goes into numerical integration is thus avoided for many bands of many systems. The necessity for the type of approximation made is discussed from the point of view of the extensive cancellation that occurs in any method of evaluating these integrals. An indication is given of the validity and applicability of the approximation and the formulae thus derived.