Bound state properties of four-body muonic quasi-atoms

TL;DR

This paper calculates the energies and properties of four-body muonic quasi-atoms, which resemble hydrogen atoms with complex nuclei, providing insights for future experimental and theoretical studies of hydrogen-like systems.

Contribution

It introduces highly accurate computational methods for four-body muonic quasi-atoms and compares their spectra to hydrogen, highlighting differences relevant for precision measurements.

Findings

Bound state spectra are similar to hydrogen but with notable differences.

Properties derived from three-body muonic ion calculations are highly accurate.

Results can aid in refining hydrogen property measurements and QED corrections.

Abstract

Total energies and various bound state properties are determined for the ground states in all six four-body muonic $a^{+} b^{+} \mu^{-} e^{-}$ quasi-atoms. These quasi-atoms contain two nuclei of the hydrogen isotopes $p^{+}, d^{+}, t^{+}$, one negatively charged muon $\mu^{-}$ and one electron $e^{-}$. In general, each of the four-body muonic $a^{+} b^{+} \mu^{-} e^{-}$ quasi-atoms, where $(a, b) = (p, d, t)$, can be considered as the regular one-electron (hydrogen) atom with the complex nucleus $a^{+} b^{+} \mu^{-}$ which has a finite number of bound states. Furthermore, all properties of such quasi-nuclei $a^{+} b^{+} \mu^{-}$ are determined from highly accurate computations performed for the three-body muonic ions $a^{+} b^{+} \mu^{-}$ with the use of pure Coulomb interaction potentials between particles. It is shown that the bound state spectra of such quasi-atoms are similar to the spectrum of the regular hydrogen atoms, but there are a few important differences. Such differences can be used in future experiments to improve the overall accuracy of current evaluations of various properties of hydrogen-like systems, including the lowest-order relativistic and QED corrections.