Electronic Transition Moment Integrals for First Ionization of CO and the A - X Transition in CO+. Some Limitations on the use of the r-Centroid Approximation.

Abstract

Integrals necessary for the determination of transition moment matrix elements from experimental data have been evaluated numerically by use of vibrational wave functions derived from RKR potentials. A power series expansion for the electronic transition moment has been assumed. The significant quantities which can be related to an arbitrary center of expansion are vibrational overlap integrals and quantities of the form ʃψ v' r n ψ v″ dr. Experimental band intensities and relative populations for vibrational levels of the initial electronic state are needed to determine the expansion coefficients. Transition moment integrals have been calculated for first ionization from the ground electronic state of CO and for the A 2Π i - X 2Σ+ transition of CO+. Comparison of these integrals with previous calculations based on Morse functions has shown them to be rather sensitive to the wave-functions [potentials] used. Characteristics generally attributed to the r-centroid and related integrals are examined, and some limitations on the use of the r-centroid approximation are discussed, following a review of assumptions made in the use of that approximation.