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We develop a theory of resonant inelastic x-ray scattering (RIXS) at the $K$edge in La$_2$CuO$_4$ on the basis of the Keldysh Green's function formalism.In our previous analysis (Phys. Rev. B 71, 035110 (2005)), the scattering bythe core-hole potential was treated within the Born approximation, and acrude-model density of states was used for the $4p$ band. We improve theanalysis by taking account of the multiple scattering in Cu3d-O$2p$ bands andby using a realistic $4p$ DOS obtained from a band calculation. The multiplescattering effect is evaluated with the use of the time representationdeveloped by Nozi\`eres and De Dominicis. It is found that the multiplescattering effect makes the $K$-edge peak in the absorption coefficient shiftto the lower energy region as a function of photon energy, that is, the photonenergy required to excite the $1s$ electron to the $K$-edge peak reduces. It isalso found that the multiple-scattering effect does not change the two-peakstructure in the RIXS spectra but modifies slightly the shape as a function ofenergy loss. These findings suggests that the multiple scattering effect couldmainly be included into a renormalization of the core-level energy and partlyjustify the Born approximation, leading to a future application to the RIXS inthree-dimensional systems.Comment: revised version with extended discussion, 24 pages, 12 figures,  accepted for PR

physical review. b, condensed matter and materials physics

Theory of resonant inelastic x-ray scattering at the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>edge in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>La</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>CuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>: Multiple scattering effects

Theory of resonant inelastic x-ray scattering at theKedge inLa2CuO4: Multiple scattering effects