The r-centroid concept revisited

The r-centroid concept, was proposed the in 1950s to permit factoring of the band strength integral Suʹ,uʹʹ into the product of the Franck-Condon factor quʹ,uʹʹ, and of the square of the electronic transition moment Re (r), when taken at the r-centroid value of the internuclear separation, r = uʹ,uʹʹ, which is the most likely value r at which the uʹ « uʹʹ transition will occur. It has been much used since then in the interpretation of intensity measurements on many band systems of importance in astrophysics, atmospheric physics, space physics, and chemical physics to determine the variation of the electronic transition moment with internuclear separation, and thereby to derive band strengths, and other molecular transition probability parameters. It has been somewhat less used in recent years in the study of individual band systems, since the development of powerful computing facilities now allow for exact ab initio numerical studies to be made of individual molecules and their radiative transitions. Nevertheless the r-centroid concept, and some of its recent developments, provide much insight into the general systematics of diatomic molecular band systems and their spectra. This partly tutorial paper reviews the origins, properties, applications, and recent developments of the r-centroid concept.