A tabulation of the bound-state energies of atomic hydrogen

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.

References in corpus (7)

• High-precision determination of the electric and magnetic form factors of the proton
• The Proton Radius Puzzle
• Nuclear recoil effect in the Lamb shift of light hydrogen-like atoms
• Electron Self Energy for Higher Excited S Levels
• Quantum electrodynamic corrections to the hyperfine structure of excited S states
• On the accuracy of the optical determination of the proton charge radius
• Self-energy values for P states in hydrogen and low-Z hydrogenlike ions

Cited by in corpus (30)

• The proton charge radius
• Theory of the Lamb shift in hydrogen and light hydrogen-like ions
• Measurement of the $2$S${}_{1/2}-8$D${}_{5/2}$ transition in hydrogen
• Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium
• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• The proton radius (puzzle?) and its relatives
• Probing new physics using Rydberg states of atomic hydrogen
• Probing New Physics with Long-Range Neutrino Interactions: An Effective Field Theory Approach
• Towards an independent determination of muon g-2 from muonium spectroscopy
• Muonic vs electronic dark forces: a complete EFT treatment for atomic spectroscopy
• Interaction of a hydrogenlike ion with a planar topological insulator
• Hyperfine splitting in ordinary and muonic hydrogen
• Measurement of the $2S_{1/2},F$=$0\to 2P_{1/2},F$=$1$ transition in Muonium
• Systematic effects important to separated-oscillatory-field measurements of the $n$$=$$2$ Lamb shift in atomic hydrogen
• Two-photon exchange on neutron and the hyperfine splitting
• Metrology of Rydberg states of the hydrogen atom
• Interference between two resonant transitions with distinct initial and final states connected by radiative decay
• Importance of nonresonant corrections for the description of atomic spectra
• Angular correlations in two-photon spectroscopy of hydrogen
• Sub-part-per-trillion test of the Standard Model with atomic hydrogen
• Properties of the Sachs electric form factor of the proton on the basis of recent $e-p$ scattering experiments and hydrogen spectroscopy
• Nuclear Predictions for $H$ Spectroscopy without Nuclear Errors
• One-electron atoms in screened modified gravity
• Relativistic Ritz approach to hydrogen-like atoms I: theoretical considerations
• Precision Nuclear-Spin Effects in Atoms: EFT Methods for Reducing Theory Errors
• Theoretical prerequisites for the upcoming generation of precision spectroscopic experiments
• Pressure Shifts in High-Precision Hydrogen Spectroscopy: I. Long-Range Atom-Atom and Atom-Molecule Interactions
• Thermal one-loop self-energy correction for hydrogen-like systems: Relativistic approach
• Classical versus quantum calculation of radiative electric quadrupole transition rates for hydrogenic states
• Fitting for the energy levels of hydrogen