Low-lying electron energy levels in three-particle electron-muon ions $(\mu e Li)$, $(\mu e Be)$, $(\mu e B)$

TL;DR

This paper calculates the electron energy level differences, including the Lamb shift and energy intervals, in muon-electron ions of lithium, beryllium, and boron using perturbation theory, accounting for various quantum effects.

Contribution

It provides analytical calculations of energy shifts in muon-electron ions, incorporating vacuum polarization, nuclear structure, and recoil effects, for comparison with future experiments.

Findings

Calculated Lamb shift (2P-2S) values for muon-electron ions.

Determined energy interval (2S-1S) in these ions.

Results agree with variational approach calculations.

Abstract

The electron Lamb shift $(2P-2S)$ and the energy interval $(2S-1S)$ in muon-electron ions of lithium, beryllium, and boron have been calculated within the framework of the perturbation theory method for the fine structure constant and the electron-muon mass ratio. The corrections of the first and second orders of the perturbation theory, which include the effects of vacuum polarization, nuclear structure and recoil, are taken into account. The obtained analytical results in perturbation theory are compared with the results of calculations within the variational approach. The obtained values for the Lamb shift $(2P-2S)$ and the interval $(2S-1S)$ can be used for comparison with future experimental data and verification of quantum electrodynamics.