# Scattering operator for elastic and inelastic resonant x-ray scattering

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 Title: Scattering operator for elastic and inelastic resonant x-ray scattering Luo, Jin Trammell, George T.; Hannon, James P. I have shown that in the fast collision approximation, the scattering operator for resonant x-ray scattering can be expressed in terms of simple spin-orbital moment operators M$\sp{(k)}$(l,s) of the valence shell involved in the resonance. Using these operators, one not only can determine the thermal expectation values of the various spin-orbit multipole moments in the valence shell through the coherent elastic scattering and absorption, but also can obtain the moment-moment correlation functions (Van Hove scattering function S(q,$\omega$)) among the various atoms of the scattering sample from the coherent elastic and inelastic scattering. We have applied the effective scattering operators to the x-ray magnetic scattering in ${La\sb{2-x}Sr\sb{x}CuO\sb4}$ high temperature superconductors, and obtained the relations between the scattering cross-section and the Van Hove scattering function, and the instantaneous correlation function of the spins in these materials. This theory is applicable to the analysis of a broad range of resonant x-ray elastic and inelastic scattering and absorption experiments involving rare earth, actinide and transition elements. Luo, Jin. (1994) "Scattering operator for elastic and inelastic resonant x-ray scattering." Doctoral Thesis, Rice University. http://hdl.handle.net/1911/16754. http://hdl.handle.net/1911/16754 1994