Two-photon absorption of optical and x-ray quanta

Two-photon absorption of an optical (laser) and an x-ray quantum is considered within the context of the Born approximation. A simple expression relating the two-photon and one-photon photoionization absorption coefficients is obtained. If the upper state is one of the conduction bands of a solid, the two-photon absorption coefficient is shown to peak at points in the zone for which the curvature of the band is a maximum. Numerical estimates show that with a 100 kW Nd laser, the intensity of the two-photon absorption process is a few percent of that of the one-photon process.