Hyperfine structure splitting for the triplet $2^{3}S(L=0)-$state in the two-muonic helium ${}^3$He ${\mu }_2$ atom

Abstract

The hyperfine structure splitting for the triplet $2^{3}S(L=0)-$state in the two-muonic helium ${}^3$He ${\mu }_2$ atom is determined to high accuracy. Such a structure arises as a result of hyperfine (or spin-spin) interaction between the triplet two-muonic shell and non-zero spin of the central helicon nucleus. Our result for the hyperfine structure splitting is $\Delta \approx 5.1623403103010\cdot 10^7$ $MHz$, where the standard uncertainty has been evaluated as $\pm 10$ $Hz$.