Generalized correspondence rules for quasi-classical dipole matrix elements

Based on the requirement of the orthogonality of quasi-classical wave functions, generalized correspondence rules are formulated for calculations of radial dipole matrix elements in the semi-classical approximation. The rules are used for the derivation of quite simple analytic representations of the oscillator strengths for electronic transitions accompanied by large variations in principal quantum numbers in the discrete and continuous spectra. Comparison with exact quantum-mechanical calculations of photoionization cross sections for alkali atoms shows the possibility of the analytic description with the help of formulas for the Cooper minimum. Conditions of the rearrangement of the hydrogen-like photorecombination spectrum are formulated for the example of the model Sommerfeld potential, and the tendency to the appearance of the inverse population of the lowest excited states is demonstrated.