Classical collisions and correspondence principle

An outstanding problem in the classical theory of atomic collisions has been its inability to produce the correct logarithmic dependence of certain excitation cross sections. The authors show that this is because the wrong correspondence has been made between classical and quantum mechanics. Bohr's correspondence principle for spontaneous transitions has been extended to include transitions induced by external fields in those situations in which quantal perturbation theory is valid and classical perturbation theory is also valid for the corresponding classical model. On applying this principle to collisions of charged particles with highly excited hydrogen atoms a high-energy (E) cross section sigma (n to n') of the correct form: sigma (n to n')=A1nE/E+B/E is obtained.