Highly excited hydrogen-atom states located in an external field near the symmetry axis of the field

Quantization rules are obtained and bands of stability loss in a strong magnetic field as well as in parallel electric and magnetic fields are observed for highly excited hydrogen states concentrated near the symmetry axis of the external field. The band boundaries are identical with the classical resonances at which a classical trajectory lying on the symmetry axis loses stability. The calculation is based on matching of the Schroedinger-equation solutions that are valid near the center of the atom with those valid at a distance from the center and concentrated near the field symmetry axis. The elements of the dipole transitions from the ground state to highly excited states are calculated. In the case of a weak magnetic field the oscillator strengths obtained agree well with the numerical calculations of Clark and Taylor [J. Phys. 13B, L737 (1980)]. For a strong magnetic field as well as for sufficiently weak parallel electric and magnetic fields the oscillator strengths show a spike near one stability-band boundary and a dip near the other