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.

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We report a novel closed-form analytic representation for the linear response relativistic wave function of the hydrogenic ns(1/2) level that is exposed to dipole radiation of frequency omega. This result is derived by means of a direct analytical solution of the inhomogeneous omega-dependent Dirac equation. The utility of the formulas obtained is demonstrated by new analytic and numerical calculations of the static and dynamic relativistic dynamic polarizabilities of the lowest hydrogenic ns(1/2) states.

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