Nonlinear Response Functions for X-Ray Laser Pulses
Response functions are macroscopic quantities that encode relevant information about interacting systems. In particular, they can provide the strength of scattering and nonlinear relaxation processes. Although nonlinear optical susceptibilities have been extensively studied, both theoretically and phenomenologically, non-linear response functions of atomic and molecular systems at x-rays wavelengths have received little attention. This scenario is likely to change with the advent of the 4th-generation light sources, the x-ray free-electron lasers (XFELs), where nonlinear effects may become observable from the interaction of these ultrahigh laser pulses and matter. In this paper, we provide a general semiclassical formalism to calculate nonlinear response functions for x-rays, which avoids the usual dipole approximations well suited for optical frequencies. Quick estimates suggest that, for x-rays frequencies, resonant nonlinear effects for atoms and in crystalline media are rather small, ranging from χ(2) ≈ 10−20 - 10−14 esu to χ(3) ≈ 10−32 - 10−19 esu. From these values, cross sections are calculated.
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