RESONANT SCATTERING: TENSORS OF HIGHER RANK AND THETA DEPENDENCE. David H. Templeton and Lieselotte K. Templeton, Department of Chemistry, University of California, Berkeley, CA 94720, USA

The resonant scattering of X rays by an atom is always anisotropic with respect to photon polarization and often changes with molecular orientation. The largest effects can be described by atomic tensors of second rank multiplied by polarization vectors for incident and scattered photons. When the finite size of the atomic wavefunctions cannot be neglected one must add tensors of higher rank with wave vectors as additional factors. A tensor of third rank is required to explain the scattering by some atoms in noncentrosymmetric sites (Phys. Rev. B 49, 14850 (1994)). This term is proportional to sinJ and does not occur in absorption spectra. It changes sign on inversion with novel consequences on structure-factor algebra. Fourth-rank effects have been observed in both absorption and scattering (e.g. Dräger, et al., Phys. Stat. Sol. (b) 146, 287 (1988); Finkelstein, et al., Phys. Rev. Lett. 69, 1612 (1992)). They can be formulated as functions of the sum and difference of the wave vectors, proportional respectively to cos²[[theta]] and sin²[[theta]]. Only the first is observed in absorption spectra. The second-rank tensor term, as derived from perturbation theory, is independent of Bragg angle. Any change of resonant scattering with Bragg angle is contained in the higher terms, but the part which is isotropic for wave vectors can be treated as a change with theta of the second-rank parameters. The semiclassical model based on a continuum of anisotropic electric susceptibility can describe only some of these properties. We study the anisotropy of these tensors by measuring the changes of intensity with azimuth of weak or "forbidden" reflections chosen to be sensitive to one term or another. New experiments with pyrite at the Fe K edge will be reported.