The surprising discrepancy between results from different methods for measuring the proton charge radius is referred to as the proton radius puzzle. In particular, measurements using electrons seem to lead to a different radius compared with those using muons. Here, a direct measurement of the n = 2 Lamb shift of atomic hydrogen is presented. Our measurement determines the proton radius to be rp = 0.833 femtometers, with an uncertainty of ±0.010 femtometers. This electron-based measurement of rp agrees with that obtained from the analogous muon-based Lamb shift measurement but is not consistent with the larger radius that was obtained from the averaging of previous electron-based measurements.

Quantum-mechanical interference with far-off-resonance neighboring states is found to cause systematic shifts for the measurements of the 2 3 P fine-structure intervals. The shifts depend on the type of experiment used to measure the intervals. Here the shifts are calculated for measurements using a single microwave pulse and for measurements using the Ramsey method of separated oscillatory fields. The shifts are small, but are large enough to affect the continuing program of determining the fine-structure constant from a comparison between accurate experimental measurements and theoretical calculations of the interval energies. The separated-oscillatory-field shifts are found to be much smaller than the single-pulse shifts.

Previous work [E. Ackad and M. Horbatsch, Phys. Rev. A 78, 062711 (2008)] on supercritical Dirac resonance parameters from extrapolated analytic continuation, obtained with a Fourier grid method, is generalized by numerically solving the coupled Dirac radial equations to a high precision. The equations, which contain the multipole decomposition of the two-center potential, are augmented by a complex absorbing potential and truncated at various orders in the partial wave expansion to demonstrate convergence of the resonance parameters in the limit of vanishing absorber. The convergence of the partial-wave spinor and of the multipole potential expansions is demonstrated in the supercritical regime. The comparison of critical distances with literature values shows that the work provides benchmark results for future two-center calculations without multipole expansion.

For many decades, improvements in both theory and experiment of the fine structure of the n = 2 triplet P levels of helium have allowed for an increasingly precise determination of the fine-structure constant. Recently, it has been observed that quantum-mechanical interference between neighboring resonances can cause significant shifts, even if such neighboring resonances are separated by thousands of natural widths. The shifts depend in detail on the experimental method used for the measurement, as well as the specific experimental parameters employed. Here, we review how these shifts apply for the most precise measurements of the helium 23P fine-structure intervals.

The resonant line shape from driving a transition between two states, |a and |b , can be distorted due to a quantum-mechanical interference effect involving a resonance between two different states, |c and |d , if |c has a decay path to |a and |d has a decay path to |b . This interference can cause a shift of the measured resonance, despite the fact that the two resonances do not have a common initial or final state. As an example, we demonstrate that such a shift affects measurements of the atomic hydrogen 2S 1/2 -to-2P 1/2 Lamb-shift transition due to 3S-to-3P transitions if the 3S 1/2 state has some initial population.