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We present a formula for the calculation of K-edge resonant inelastic x-rayscattering on transition metal compounds, based on a local interaction betweenthe valence shell electrons and the $1s$ core hole. Extending a previousresult, we include explicit momentum dependence and a basis with multiplecore-hole sites. We apply this formula to a single-layered charge, orbital andspin ordered manganite, La$_{0.5}$Sr$_{1.5}$MnO$_4$, and obtain good agreementwith experimental data, in particular with regards to the large variation ofthe intensity with momentum. We find that the screening inLa$_{0.5}$Sr$_{1.5}$MnO$_4$ is highly localized around the core-hole site anddemonstrate the potential of K-edge resonant inelastic x-ray scattering as aprobe of screening dynamics in materials.

Momentum dependence in K-edge resonant inelastic x-ray scattering and its application to screening dynamics in CE-phase La$_{0.5}$Sr$_{1.5}$MnO$_4$