Quantum chaos in multicharged ions and statistical approach to the calculation of electron-ion resonant radiative recombination

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