Intermediate-and strong-coupling approximations for scattering in a laser field

A study is made of the range of applicability of various versions of the low-frequency approximation for electron-atom scattering in a laser field. A key physical parameter: the ratio of the electron-field interaction energy to the photon energy: is identified and a distinction is drawn between two regimes, corresponding to values of this ratio of order unity (intermediate coupling) and values large compared to unity (strong coupling). Separate derivations are given which are appropriate to one or the other of these regimes, with proper account taken of the possibility of resonances or composite bound-state poles in the field-free scattering amplitude. The strong-coupling case is characterized by the emission or absorption of large numbers of virtual soft photons in initial and final states. The analogy with the problem of spontaneous infrared radiation which this physical picture suggests is put into more precise form here through the derivation of sum rules for the total cross section and for the average energy transferred to the field. The strong-coupling approximation is closely related to the approximate treatment, due to Keldysh and others, of multiphoton ionization as a tunneling process. This relation is demonstrated explicitly here by recognizing that ionization may be thought of asmore » the second half of an induced resonance reaction and applying, to the amplitude obtained in this way, some of the approximation techniques developed for the scattering problem.« less