The hyperfine structure of the ground states in the helium-muonic atoms

The hyperfine structures of the ground states in the He2+3μ−e− and He2+4μ−e− helium-muonic atoms are investigated with the use of highly accurate variational wave functions. The differences between corresponding levels of hyperfine structure (i.e. hyperfine splittings) are determined to very high numerical accuracy. In particular, we have found that the hyperfine structure splitting in the ground state of the He2+4μ−e− atom is Δν≈4464.55454(3) MHzΔν≈4464.55454(3) MHz, while analogous splitting for the He2+3μ−e− atom is Δν≈4166.43547(3)Δν≈4166.43547(3).

► The hyperfine structures of the ground states in the He2+3μe and He2+4μe helium-muonic atoms are investigated.
► The hyperfine structure splittings (HFS) are determined to very high numerical accuracy.
► HFS in the ground state of the He2+3,4μ−e− atoms are Δν≈4464.55438(1) MHzΔν≈4464.55438(1) MHz and Δν≈4166.43532(1)Δν≈4166.43532(1), respectively.
► Our results agree with the known experimental results for these atoms.