Accurate radial atomic model potentials by means of a novel RKR-QDT combined approach
Abstract:The age-old semiclassical Rydberg-Klein-Rees (RKR) inverse spectrum method, which has been, so far, widely applied to diatomic molecules only, is combined with the quantum defect theory (QDT) formalism so that highly accurate radial model potentials supporting experimental bound spectra of atoms and atomic ions are constructed. There are two main steps in our approach. The first step consists in constructing, by inversion, the best first-order WKB potential. The high quality of this potential is attested by the fact that the standard WKB quantization condition for bound states perfectly reproduces the input data. The second step deals with how to improve further, on a quantum-mechanical level, this RKR potential energy so that the eigenvalues of the radial Schrödinger equation for the quantum-mechanical analogue of the RKR curve, obtained from the latter after subtraction of Langer's correction, are in agreement with the input data. To this purpose, a rapidly converging iterative QDT procedure is developed, according to which the input quantum defects are, at each iteration, corrected by the difference between the experimental and the calculated quantum defects. The so-constructed converged potential curves are able to reproduce with spectroscopic accuracy the bulk of available experimental spectra. Demonstrative examples from the structure of the high-l 9snl series of Ba and for selected low-l Rydberg series of the Ba+ion are given.
Document Type: Miscellaneous
Affiliations: 1: Institute of Accelerating Systems and Applications, University of Athens, PO Box 17214, GR-10024 Athens, Greece 2: Laboratoire des Propriétés Optiques des Matériaux et Applications, UMR CNRS 6136, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers, France
Publication date: April 1, 2002