Resonant inelastic X-ray scattering (RIXS) using the Cu K shell of one-dimensional cuprates is compared with that using the O K shell on the basis of numerically-exact diagonalization calculations applied for a finite-size cluster model. Particular attention is paid to the effects of Cu 3d orbital degeneracy on the Cu K RIXS and the incident photon energy dependence of the Cu K RIXS. Inclusion of the Cu 3d(3z 2 - r 2) orbital results in the dd excitation in the Cu K RIXS, which is in accordance with the O K RIXS. However the excitation mechanism differs for the Cu K RIXS and O K RIXS. The dd excitation in the Cu K RIXS is caused through the mixing between the Zhang-Rice singlet (ZRS) and Cu 3d(3z 2 - r 2) bands, while it is mainly caused by the optical dipole transition process in the case of O K RIXS. Moreover, mixing between the ZRS and Cu 3d(3z 2 - r 2) bands induces new structures, whose binding energy is higher than that of the structure due to electron-hole pair excitations from the ZRS band to the upper Hubbard band. The angle-resolved photoemission calculation confirms that the mixing between the Cu 3d(3z 2 - r 2) and ZRS bands is appreciable around the Brillouin zone center in the case of corner-share-type crystal structure.
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