Semiclassical formula for oscillator strengths of atomic spectra in external fields

In a previous Rapid Communication [Phys. Rev. A 56, R5 (1997)] we reported a semiclassical formula describing oscillator strengths for transitions to a high Rydberg state of a hydrogen atom in an electric field. The formula relates the oscillator strength for an atomic transition into a Rydberg state to the angular distribution of outgoing electron waves and to the density of classical tori. Here we give a derivation of that formula and we suggest some generalizations. We compare the formula with experimental measurements of the absorption spectrum of hydrogen in an electric field. This absorption spectrum consists of quasidiscrete resonances superposed on a smooth background. We find that this background has a hitherto unexplained structure that was visible but not recognized in the experiment. The background absorption is related to electron orbits that directly escape from the atom, and its structure is related to the angular distribution of outgoing electrons.