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The longstanding problem of interpretation of satellite structures in corelevel photoemission spectra of metallic systems with a low density ofconduction electrons is addressed using the specific example of Sb-dopedSnO$_2$. Comparison of {\it ab initio} many-body calculations with experimentalhard X-ray photoemission spectra of the Sn 4$d$ states shows that strongsatellites are produced by coupling of the Sn core hole to the plasmaoscillations of the free electrons introduced by doping. Within the sametheoretical framework, spectral changes of the valence band spectra are alsorelated to dynamical screening effects. These results demonstrate that, for theinterpretation of electron correlation features in the core level photoelectronspectra of such narrow-band materials, going beyond the homogeneous electrongas electron-plasmon coupling model is essential.

Revisiting the origin of satellites in core level photoemission of transparent conducting oxides: the case of $n$-doped SnO$_2$