"Multiple-" versus "multi-" photon absorption in the theory of resonant ionization

The author has identified his result for resonant ionization by the simultaneous absorption of two photons by a ground-state electron [Phys. Rev. A 17, 659 (1978)] with the high-laser-power large-intermediate-state ionization rate result derived by Eberly and co-workers using a steady-state rate theory. This result gives Rσ₂₂ for all power levels considered, where R is the one-photon ionization rate for the intermediate state and σ₂₂ is its steady-state population factor. The result can be cast in this form, but it is found that σ₂₂ must be much less than σ₁₁, the ground-state population factor. Thus the resonant process can be described by a rate limit for conserving energy by simultaneous absorption only when the ground-state population factor remains unity to order Ω²R², where Ω is the Rabi rate for the bound-bound transition. In other words, the simultaneous and sequential processes are physically equivalent in this limit.