Relativistic Ritz approach to hydrogenlike atoms: Theoretical considerations

The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before advent of mechanics, yet this approach remained limited by its nonrelativistic foundation. Here I present long-distance relativistic effective theory describing hydrogenlike systems arbitrary mass ratios, thereby extending canonical Ritz-like approach. Fitting to hydrogen energy levels predicted bound-state QED indicates that it is superior canonical, An analytic analysis reveals nonlinear consistency relations within level predictions relate higher-order corrections those at lower order, providing guideposts for future perturbative calculations as well insights into asymptotic behavior Bethe logarithm. Applications include fitting spectroscopic data, allowing determination fine-structure constant from large spectral data sets and also check internal independently QED.