Hyperfine splitting computation in the 1s1/2(e)2s1/2(mu) state of the exotic (4He2+ - mu-e-)0 and (3He2+ - mu-e-)0 atoms

An ab initio calculation of the hyperfine splitting (HFS) intervals in the 2s1/2(mu)1s1/2(e) state of the exotic (4He2+ - mu-e-)0 and (3He2+ - mu-e-)0 atoms is carried out. The smallness of beta = me/mmu approximately 1/200 (the electron and the mu-meson mass ratio) enables us to take into account the non-relativistic interparticle correlational interaction perturbatively. Corresponding corrections, which give the dominant contribution to the HFS, are calculated to logarithmic accuracy analytically and exactly. Together with the leading relativistic and radiative corrections the HFS values obtained turn out to be in accord with the results of other calculations.