Measurements of Polarization Dependencies in Parametric Down-Conversion of X-rays into Ultraviolet Radiation

We present measurements of the polarization dependencies of the x-ray signal photons generated by the effect of parametric down-conversion of x rays into ultraviolet radiation. The results exhibit pronounced discrepancies with the classical model for the nonlinearity but qualitatively agree with a newly developed quantum mechanical theory for the nonlinear interaction. Our work shows that the reconstruction of the atomic scale charge distribution of valence electrons in crystals by using nonlinear interaction between x rays and longer wavelength radiation, as was suggested in previous works, requires the knowledge of polarization of the generated x-ray signal beam. The results presented in this work indicate a new methodology for the study of properties of the Wannier functions in crystals.