We report bulk-sensitive hard X-ray ($h u$ = 5.95 KeV) core level photoemission spectroscopy (PES) of single crystal V$_{1.98}$Cr$_{0.02}$O$_{3}$ and the high-$T_c$ cuprate Bi$_2$Sr$_{2}$CaCu$_{2}$O$_{8+delta}$ (Bi2212). V$_{1.98}$Cr$_{0.02}$O$_{3}$ exhibits low binding energy satellites to the V $2p$ main lines in the metallic phase, which are suppressed in the antiferromagnetic insulator phase. In contrast, the Cu $2p$ spectra of Bi2212 do not show temperature dependent features, but a comparison with soft X-ray PES indicates a large increase in the $2p^5 3d^9$ satellites or $3d^9$ weight in the bulk. Cluster model calculations, including full multiplet structure and a screening channel derived from the coherent band at the Fermi energy, give very satisfactory agreement with experiments.
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