Chaos-induced enhancement of resonant multielectron recombination in highly charged ions: Statistical theory

Abstract

A statistical theory of resonant multielectron recombination based on properties of chaotic eigenstates is developed. The level density of many-body states increases exponentially with the number of excited electrons. When the residual electron-electron interaction exceeds the interval between these levels, the eigenstates (called compound states or compound resonances if these states are in the continuum) become ``chaotic'' superpositions of large numbers of Hartree-Fock configurational basis states. This situation takes place in some rare-earth atoms and many open-shell multiply charged ions excited in the process of electron recombination. Our theory describes resonant multielectron recombination via dielectronic doorway states leading to such compound resonances. The result is a radiative capture cross section averaged over a small energy interval containing several compound resonances. In many cases individual resonances are not resolved experimentally (since the interval between them is small, e.g., $\ensuremath{\le}$1 meV, possibly even smaller than their radiative widths); therefore, our statistical theory should correctly describe the experimental data. We perform numerical calculations of the recombination cross sections for tungsten ions W${}^{q+}$, $q=18$--25. The recombination rate for W${}^{20+}$ measured recently [Schippers et al. Phys. Rev. A 83, 012711 (2011)] is ${10}^{3}$ greater than the direct radiative recombination rate at low energies, and our result for W${}^{20+}$ agrees with the measurements.