We show that the spectrum and eigenstates of open-shell multicharged atomic ions near the ionisation threshold are chaotic, as a result of extremely high level densities of multiply excited electron states (103 eV–1 in Au24+) and strong configuration mixing. This complexity enables one to use statistical methods to analyse the system. We examine the dependence of the orbital occupation numbers and single-particle energies on the excitation energy of the system, and show that the occupation numbers are described by the Fermi–Dirac distribution, and the temperature and chemical potential can be introduced. The Fermi–Dirac temperature is close to the temperature defined through the canonical distribution. Using a statistical approach we estimate the contribution of multielectron resonant states to the radiative capture of low-energy electrons by Au25+ and demonstrate that this mechanism fully accounts for the 102 times enhancement of the recombination over the direct radiative recombination, in agreement with recent experimental observations.