  We show that the spectrum and eigenstates of open-shell multicharged atomic
ions near the ionization threshold are chaotic, as a result of extremely high
level densities of multiply excited electron states ($10^3 eV^{-1}$ in
Au^{24+}) 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 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 Au^{25+} and demonstrate that this mechanism fully
accounts for the 10^2 times enhancement of the recombination over the direct
radiative recombination, in agreement with recent experimental observations.
