A tabulation of the bound-state energies of atomic hydrogen

TL;DR

This paper provides detailed tables of atomic hydrogen bound-state energies including hyperfine structure corrections, achieving high accuracy thanks to recent proton radius measurements, and extends previous work by incorporating these effects.

Contribution

It presents new comprehensive tables of hydrogen energy levels with hyperfine corrections, including effects of the proton radius, which were not included in earlier works.

Findings

Energy uncertainties less than 1 kHz for all states

Inclusion of hyperfine structure corrections due to electron and proton properties

Comparison of theoretical energies with recent precision measurements

Abstract

We present tables for the bound-state energies for atomic hydrogen. The tabulated energies include the hyperfine structure, and thus this work extends the work of Rev. Mod. Phys. {\bf 84}, 1527 (2012), which excludes hyperfine structure. The tabulation includes corrections of the hyperfine structure due to the anomalous moment of the electron, due to the finite mass of the proton, and due to off-diagonal matrix elements of the hyperfine Hamiltonian. These corrections are treated incorrectly in most other works. Simple formulas valid for all quantum numbers are presented for the hyperfine corrections. The tabulated energies have uncertainties of less than 1 kHz for all states. This accuracy is possible because of the recent precision measurement [Nature, {\bf 466}, 213 (2010); Science, {\bf 339}, 417] of the proton radius. The effect of this new radius on the energy levels is also tabulated, and the energies are compared to precision measurements of atomic hydrogen energy intervals.