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Theory of resonant inelastic X-ray scattering. Model. Conclusions. Cross section. Dipole operator. L.J.P. Ament, F. Forte, J. van den Brink Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands. Abstract.

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  1. Theory of resonant inelastic X-ray scattering Model Conclusions Cross section Dipole operator L.J.P. Ament, F. Forte, J. van den Brink Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands Abstract The cross section for indirect resonant inelastic X-ray scattering (RIXS) on the K-edge of transition metal ions is derived. It turns out to be a linear combination of the charge response function and the dynamic longitudinal spin density function. This result is asymptotically exact for both strong and weak local core-hole potentials and constitutes a smooth interpolation in between these limits. The relative charge and spin contribution to the inelastic spectral weight can be changed by varying the incident photon energy. cond-mat/0609767 RIXS Results Core electron is excited Core-hole + excited electron induce potential Fermi-surface electrons interact with this potential After a short time: relaxation Spinless ‘fermions’: (T = 0 K) See below! Density correlation function, Spin-1/2 fermions: Dynamic longitudinal spin correlation function Simplest case = spinless fermions: They interact with the core-hole: P1,2 practically T-independent! T-dependence in structure factors. No monopole due to local exciton: interaction drops off rapidly. Approximate: Cross section is given by Kramers-Heisenberg formula:1 Adjust detuning in to see either spin or charge correlation! Multi-band systems. Example: transition metal with 3d and 4s band. with Scattering amplitude Energy conservation • Various scattering cross sections are expressed in terms of the dynamical charge and spin correlation functions. These are exact for strong and weak core-hole potentials U. • The resonant prefactors are weakly temperature dependent. • On the basis of our results, the charge and spin structure factor of e.g. Hubbard-like model Hamiltonians can be directly compared to the experimental RIXS spectra. Intermediate states are short-lived: energy broadening  is large, thus many intermediate states can be reached. Use spectral decomposition (after some manipulations) to obtain an exact solution for both strong and weak U. [1] H.A. Kramers and W. Heisenberg, Z. Phys. 31, 681 (1925)

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