In x-ray photoelectron spectroscopy (XPS), the injected hole interacts with the electronic polarization cloud induced by the hole itself, ultimately resulting in a lower binding energy. Such a polarization effect can shift the core-level energy by more than 1 eV, as shown here by embedded many-body perturbation theory for the paradigmatic case of noble-gas clusters made of Ar, Kr, or Xe. The polarization energy is almost identical for the different core orbitals of a given atom, but it strongly depends on the position of the ionized atom in the cluster. An analytical formula is derived from classical continuum electrostatics, providing an effective and accurate description of polarization effects, which permits to achieve an excellent agreement with available experiments on noble-gas clusters at a modest computational cost. Moreover, the analytical formula is transferable to other insulating systems, as demonstrated by carbon $1s$ in the diamond cluster. Electronic polarization provides a crucial contribution to the core-level absolute energies and chemical shifts.

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• Electronic structure
• Nanoclusters
• Quantum many-body systems
• GW method
• Many-body techniques
• X-ray photoelectron spectroscopy