We develop a theory of resonant inelastic x-ray scattering (RIXS) at the $K$ edge in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ on the basis of the Keldysh Green’s function formalism. In our previous analysis [Phys. Rev. B 71, 035110 (2005)], the scattering by the core-hole potential was treated within the Born approximation, and a crude-model density of states (DOS) was used for the $4p$ band. We improve the analysis by taking account of the multiple scattering in $\mathrm{Cu}3d\text{−}\mathrm{O}2p$ bands and by using a realistic $4p$ DOS obtained from a band calculation. The multiple scattering effect is evaluated with the use of the time representation developed by Nozières and De Dominicis. It is found that the multiple scattering effect makes the $K$-edge peak in the absorption coefficient shift to the lower-energy region as a function of photon energy, that is, the photon energy required to excite the $1s$ electron to the $K$-edge peak reduces. It is also found that the multiple-scattering effect does not change the two-peak structure in the RIXS spectra but modifies slightly the shape as a function of energy loss. These findings suggest that the multiple scattering effect could mainly be included into a renormalization of the core-level energy and partly justify the Born approximation, leading to a future application to the RIXS in three-dimensional systems.

• Received 10 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.245122