On hyperfine structure of the rotationally excited $1s_{\mu }n{\ell }_e$-states in helium muonic atoms

Abstract

The new approach is develop to determine the hyperfine structure of the rotationally excited $1s_{\mu }n{\ell }_e$-states in the three-body helium muonic ${}^3$He $\mu e$ and ${}^4$He $\mu e$ atoms. The formulas derived in this study allow one to evaluate the hyperfine structure splittings for an arbitrary rotationally excited (bound) $1s_{\mu }n{\ell }_e$-state in the three-body helium muonic atoms. Similar formulas have never been produced in earlier studies and this explains why these hyperfine structure splittings are still unknown for these bound states.