  We present a detailed Cu K-edge resonant inelastic X-ray scattering (RIXS)
study of the Mott insulator La2CuO4 in the 1-7 eV energy transfer range. As
initially found for the high-temperature superconductor HgBa2CuO4+d, the
spectra exhibit a multiplet of weakly-dispersive electron-hole excitations,
which are revealed by utilizing the subtle dependence of the cross section on
the incident photon energy. The close similarity between the fine structures
for in-plane and out-of-plane polarizations is indicative of the central role
played by the 1s core hole in inducing charge excitations within the CuO2
planes. On the other hand, we observe a polarization dependence of the spectral
weight, and careful analysis reveals two separate features near 2 eV that may
be related to different charge-transfer processes. The polarization dependence
indicates that the 4p electrons contribute significantly to the RIXS cross
section. Third-order perturbation arguments and a shake-up of valence
excitations are then applied to account for the final-energy resonance in the
spectra. As an alternative scenario, we discuss fluorescence-like emission
processes due to 1s -> 4p transitions into a narrow continuum 4p band.
