Coherent metallic screening structures shown in core-level photoemission spectra for strongly correlated oxide materials were studied by hard x-ray photoemission spectroscopy (HAXPES) and the configuration interaction (CI) theory based on the cluster model, including the coherent metallic screening process. For the La${}_{1\ensuremath{-}x}$Ba${}_{x}$MnO${}_{3}$ thin film, the normalized intensity of the coherent metallic screening structure (${I}_{S}$) seen in the Mn 2$p$ core-level spectra was proportional to the square of the hybridization strength, ($V$*), between the transition metal 3$d$ and coherent metallic states. In contrast, the normalized ${I}_{S}$ seen in the V 2$p$ core-level spectra for the V${}_{1\ensuremath{-}x}$W${}_{x}$O${}_{2}$ thin film was not proportional to ($V$*). The different behaviors of the normalized ${I}_{S}$ for the La${}_{1\ensuremath{-}x}$Ba${}_{x}$MnO${}_{3}$ and V${}_{1\ensuremath{-}x}$W${}_{x}$O${}_{2}$ thin films as a function of $V$* were understood by the series of the CI cluster model calculation. From the CI cluster model calculation, we found that the charge transfer energy (\ensuremath{\Delta}*) between the transition metal 3$d$ states and the coherent metallic states strongly affect the normalized ${I}_{S}$ in the 2$p$ core-level photoemission final states. Therefore, the behavior of the normalized ${I}_{S}$ in the 2$p$ core-level HAXPES is thus not simply explained by the change of $V$*. The electronic structure parameters such as \ensuremath{\Delta}* and $V$* relating to the coherent metallic states strongly contribute to the variation of the normalized ${I}_{S}$ in the photoemission final states. In contrast, we found that the detailed ${I}_{S}$ evaluation in the core-level HAXPES experiments for materials, in which the coherent metallic screening structures appear, allows us to evaluate the value of $V$* when we have the experimental core-level spectra and the electronic structure parameters set for a reference material. We also found that the intensity at the Fermi level is proportional to ($V$*), as expected from the Anderson impurity model.
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