Hyperfine-structure splitting in the triplet states of carbon muonic ions

Abstract

Hyperfine-structure splittings in the ${2}^{3}S(L=0)$ state of the six-body carbon muonic ${^{11}\text{C}}^{6+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}_{4}^{\ensuremath{-}}$, ${^{12}\text{C}}^{6+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}_{4}^{\ensuremath{-}}$, ${^{13}\text{C}}^{6+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}_{4}^{\ensuremath{-}}$, and ${^{14}\text{C}}^{6+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}_{4}^{\ensuremath{-}}$ ions are determined numerically with the use of variational wave functions. The variational wave functions for each of these carbon muonic ions are constructed with the use of six-body Gaussoids which explicitly depend upon all 15 relative coordinates ${r}_{12},{r}_{13},\dots{},{r}_{56}$ defined in an arbitrary six-body system.