Nonvariational calculation of the hyperfine splitting and other properties of the ground state of the muonic3He atom

Abstract

The properties of the ground state of the muonic helium atom $e\ensuremath{\mu}{}^{3}{\mathrm{He}}^{2+}$ have been calculated nonvariationally, using the correlation function hyperspherical harmonic method utilizing a nonlinear parametrization of the correlation function. The parametrization is similar to the one used in an earlier paper for $e\ensuremath{\mu}{}^{4}{\mathrm{He}}^{2+}$ but the differences in the convergence were found to be important for the choice of optimal parameters. The parametrization is especially suited to accelerate the convergence of singular operators. As a result, the obtained expectation values of the $\ensuremath{\delta}({\mathbf{r}}_{k})$ operators have error margins smaller than the differences in the literature. The lowest-order hyperfine splitting, which depends on the fine structure constant and on the magnetic moment of the ${}^{3}{\mathrm{He}}^{2+}$ nucleus, is compared with values in the literature.