Related papers: Fitting for the energy levels of hydrogen
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 method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between…
The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic…
We present numerical values for the self-energy shifts predicted by QED (Quantum Electrodynamics) for hydrogenlike ions (nuclear charge $60 \le Z \le 110$) with an electron in an $n=3$, 4 or 5 level with high angular momentum ($5/2\le j \le…
By using a Coulomb potential modified by the interaction between the magnetic moments of the electron and proton, we have calculated the energy levels of a hydrogen atom. We have obtained fine structure, hyperfine structure and the Lamb…
This paper calculates the quantized energy levels of the hydrogen atom, using a metaplectic-c prequantization bundle and a definition of a quantized energy level that was introduced by the author in a previous paper. The calculation makes…
Quantum electrodynamics (QED), the first relativistic quantum field theory, describes light-matter interactions at a fundamental level and is one of the pillars of the Standard Model (SM). Through the extraordinary precision of QED, the SM…
The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated…
Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other. Two reasons justify a further look at this subject: 1) One of the approximations used in…
The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching…
A long-distance effective theory of hydrogen-like atoms, dubbed the relativistic Ritz approach was recently introduced and some its theoretical consequences were explored. In this article, the relativistic Ritz approach is used to fit…
The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom…
Ground-state hyperfine splittings in hydrogen and muonium are very well measured. Their difference, after correcting for magnetic moment and reduced mass effects, is due solely to proton structure--the large QED contributions for a…
The available experimental information on the Range-Energy relation for protons stopped in hydrogen gas is summarized in the SRIM software package. The estimated precision of this data is several percents. Here we describe a possibility to…
The "catastrophe" in solving the Dirac equation for an electron in the field of a point electric charge, which emerges for the charge numbers Z > 137, is removed in this work by effective accounting of finite dimensions of nuclei. For this…
We argue that the proton's charge-radius contributes differently to shifts of Hydrogen-like energy levels than naively expected due to an incorrect choice for the boundary condition at the proton's position in standard calculations. In…
Comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogen-like ions can yield information on values of fundamental constants and test theory. With the results of a calculation…
The first fully relativistic, rigorous QED calculations of the self-energy correction to the fine-structure levels of heavy muonic atoms are reported. We discuss nuclear model and parameter dependence for this contribution as well as…
While measurements of the hyperfine structure of hydrogen-like atoms are traditionally regarded as test of bound-state QED, we assume that theoretical QED predictions are accurate and discuss the information about the electromagnetic…
Precision spectroscopy of the hydrogen molecule is a test ground of quantum electrodynamics (QED), and may serve for determination of fundamental constants. Using a comb-locked cavity ring-down spectrometer, for the first time, we observed…