Semiclassical Formula for Oscillator Strengths in Atomic Spectra

A simple semiclassical formula is given for the oscillator strengths of high Rydberg states of a hydrogen atom in an electric field. The oscillator strength of a state is proportional to the square of the function representing the quantum angular distribution of outgoing waves, evaluated at the classical angle of ejection from the atom that sends the electron into a semiclassically quantized eigentrajectory. The formula gives an interpretation of the envelopes of Stark manifolds in photoabsorption spectra; it is in good agreement with quantum calculations. The formula may also be used for other integrable or near-integrable systems