Quantum defects for highly stripped ions

A version of quantum-defect theory appropriate to the analysis of the spectra of highly ionised atoms is obtained from the single-electron Dirac equation. Quantum defects mu _n are defined as the principal quantum number n increases along the Rydberg series using Sommerfeld's relativistic one-electron energy level formula. Considering the analytic properties of solutions to the Dirac equation, the authors establish that mu _n can be extended smoothly away from the bound-state energies just as in the non-relativistic theory. Moreover, the relativistic mu ( epsilon ) can be analytically continued beyond the threshold epsilon =mc² and related to the non-Coulomb scattering phaseshift delta ( epsilon ). At the threshold the authors establish the result delta (mc²)= pi mu (mc²) well known in non-relativistic quantum-defect theory. Several examples of the relativistic quantum-defect theory are given for highly stripped Na-like and Li-like ions.