Nonvariational calculation of the hyperfine splitting and other properties of the ground state of the muonic 3He atom

The properties of the ground state of the muonic helium atom e mu He-3(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 mu He-4(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 delta(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 He-3(2+) nucleus, is compared with values in the literature.