The Hyperfine Structure of the Ground State in the Muonic Helium Atoms

Non-relativistic ionization energies 3 He 2+ μ − e − and 4 He 2+ μ − e − of helium-muonic atoms are calculated for ground states. The calculations are based on the variational method of the exponential expansion. Convergence of the variational energies is studied by an increasing of a number of the basis functions N. This allows to claim that the obtained energy values have 26 significant digits for ground states. With the obtained results we calculate hyperfine splitting of the muonic helium atoms.