Nonlinear response of bound electrons to x rays

In the high-frequency limit, general expressions for second- and third-order induced electronic current densities in a medium are derived. These are valid for any medium with arbitrary spatial electronic-density variations. It is shown that the second-order current density at x-ray frequencies depends directly on the gradient of the unperturbed electronic density, so that it is sensitive to density variations both near the surface and near the ionic cores in a solid.