Bound state properties of four-body muonic quasi-atoms

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.

References in corpus (1)

• Bound state spectra of three-body muonic molecular ions

Cited by in corpus (1)

• On the weakly-bound (1,1)-states in the three-body $dd\mu$ and $dt\mu$ muonic ions