  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 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.
Electronic polarization provides a crucial contribution to core levels absolute
energies and chemical shifts.
