Transformation of the spectrum of atomic hydrogen in crossed electric and magnetic fields

The spectrum of highly excited atomic hydrogen in weak mutually orthogonal electric and magnetic fields is investigated. An analytical description is given for the splitting of levels remaining degenerate in the first order of perturbation theory. Approximate expressions are obtained for the energy eigenvalues and for the exponentially small tunnelling splitting of doublet states. It is shown that the spectrum is radically transformed when the relative strength of the two fields is changed.