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

Abstract

The hyperfine structure splitting for the triplet $2^{3}S(L = 0)-$state in the two-muonic helium ${}^{3}$He $μ_{2}$ 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 $Δ\approx 5.1623403103010 \cdot 10^{7}$ $MHz$, where the standard uncertainty has been evaluated as $\pm 10$ $Hz$.