A two-isotope higher-order RKR-type inversion procedure

The Rydberg-Klein-Rees (RKR) method is a valuable everyday tool for determining diatom potential energy curves. However, the RKR method is based upon the first-order WKB approximation, and while in most cases the potential curves it yields are adequate, there exist situations in which their deficiencies are unacceptable. This work addresses the above problem by presenting and testing a new higher-order, RKR-like inversion procedure which is exact within the third-order WKB approximation. The new method relies upon the existence of data for two isotopes. The turning point expressions obtained in the new method have exactly the same structure as the ordinary RKR expressions, and the procedure requires no iteration. Tests for two well-defined model problems show that the present method can yield potentials which are more accurate than those obtained from first-order RKR calculations, independent of whether or not the latter includes the widely used Kaiser correction.