  X-ray photoelectron spectroscopy (XPS) measures electron removal energies,
providing direct access to core and valence electron binding energies, hence
probing the electronic structure. In this work, we benchmark for the first time
the ab initio many-body GW approximation on the complete electron binding
energies of noble gas atoms (He-Rn), which spans 100~keV. Our results
demonstrate that GW achieves an accuracy within 1.2% in XPS binding energies,
by systematically restoring the underestimation from density-functional theory
(DFT, error of 14%) or the overestimation from Hartree-Fock (HF, error of
4.7%). Such results also imply the correlations of $d$ electrons are very well
described by GW.
