The Vibrational Overlap Integral and the Intensities in Band Systems of Diatomic Molecules

For the evaluation of the so-called vibrational overlap integral in the theory of the relative intensities in a band system of a diatomic molecule various approximate methods have been proposed for obtaining the vibrational wave functions. The ` distorted wave ' method of Gaydon, Pearse and Pillow is here discussed. For the case of Morse oscillators an approximate method is suggested that enables the integrals to be evaluated semi-analytically. The method is applied to the calculation of the relative intensities of the second negative bands of O 2 + studied recently experimentally by Feast. A procedure for applying the WKB method to find the vibrational wave functions of an anharmonic oscillator is also given. A general exact relation involving the vibrational wave functions of two electronic states and their potentials is given which may be used as a check for the accuracy of the approximate wave functions obtained by various methods.