Comparison of phenomenological and supersymmetry-inspired quantum-defect methods in their relativistic and quasirelativistic formulations

Abstract

The comparison of phenomenological and supersymmetry-inspired quantum-defect methods in their relativistic and quasirelativistic formulations is undertaken through a systematic study. Derivations, which emphasize similarities and differences between these approaches, are applied to evaluate oscillator strengths for low-lying and Rydberg states for lithiumlike, sodiumlike, and copperlike ions. Relativistic transition matrix elements calculated with the Dirac wave functions are gauge invariant. For the quasirelativistic formalism, an effective transition operator in the velocity gauge is proposed for the calculations. The detailed numerical results we obtained enable us to draw inferences as to the improvements and also to the limitations of these models.