"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 $R{\sigma }_{22}$ for all power levels considered, where $R$ is the one-photon ionization rate for the intermediate state and ${\sigma }_{22}$ is its steady-state population factor. The result can be cast in this form, but it is found that ${\sigma }_{22}$ must be much less than ${\sigma }_{11}$, 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 $\frac{{\Omega }^2}{R^2}$, where $\Omega$ is the Rabi rate for the bound-bound transition. In other words, the simultaneous and sequential processes are physically equivalent in this limit.