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The availability of extraordinarily bright femtosecond ultraviolet sources is rapidly extending the study of nonlinear atomic responses into an unexplored regime involving intensities in the range of ∼ 10^20 W/cm 2. An estimate is made, covering approximately ten orders of magnitude in intensity, of the effective cross section <σNγ> for nonlinear energy transfer to atoms undergoing subpicosecond irradiation. This treatment, which includes : (a) threshold measurements for low stages of ionization in the low intensity regime (< 10^14 W/cm 2), (b) the experimentally determined average cross section for total energy transfer at an intermediate intensity (∼ 10^16 W/cm 2), and (c) theoretical estimates for the strong field regime (> 10^19 W/cm2), indicates that the cross section for energy transfer in the high intensity (> 10^19 W/cm2) high Z limit falls in a relatively narrow range between simply established upper and lower bounds. The values of these limits are σm = 8 π λ2 c (upper) and the magnitude of the total photoabsorption cross section of Cf at the K edge (lower). Based on this analysis, the maximum cross section for heavy atoms in the high intensity limit is expected to be approximately <σ Nγ> max ∼ 10^-20 cm2, a value which represents an energy transfer rate of ∼ 1 W/atom for an assumed intensity of 10^20 W/cm2. Coupling of this strength would enable the creation of highly energetic and strongly nonequilibrium states of matter and motivates the conclusion that stimulated emission in the X-ray range can be generated by these means

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