Relativistic Corrections to the Energy of the Electron in a Hydrogenlike Atom

В. В. Скобелев

James T. Cushing

An elementary but rigorous treatment is given of the Bohr model of hydrogenlike atoms in which first-order corrections are made for both the finite mass of the nucleus and for the relativistic motion of the electron. Particular attention is paid to the approximations necessary to obtain the energy levels first given by Sommerfeld.

O. Ya. Savchenko

Roger Boudet

Niklas Michel, Jacek Zatorski, Christoph H. Keitel

In the relativistic description of atomic systems in external fields, the total momentum and the external electric field couple to the angular momentum of the individual particles. Therefore, the motional state of an ion in a particle trap influences measurements of internal observables such as energy levels or the $g$ factor. We calculate the resulting relativistic shift of the Larmor frequency and the corresponding $g$-factor correction for a bound electron in a hydrogenlike ion in the $1 S$ state due to the ion moving in a Penning trap and show that it is negligible at the current precision of measurements. We also show that the analogous energy shift for measurements with an ion in the ground state of a Paul trap vanishes in leading order.

A. Surzhykov, José Paulo Santos, Pedro Manuel Duarte Gonçalves Amaro +1 more

Two-photon decay of hydrogenlike ions is studied within the framework of second-order perturbation theory, based on the relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative-energy (intermediate virtual) states that occur in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ and $2{p}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ transitions in neutral hydrogen H as well as for hydrogenlike xenon ${\text{Xe}}^{53+}$ and uranium ${\text{U}}^{91+}$ ions. We found that for a correct evaluation of the total and energy-differential decay rates, summation over the negative-energy part of Dirac's spectrum should be properly taken into account both for high-$Z$ and low-$Z$ atomic systems.