Level-resolved quantum statistical theory of electron capture into many-electron compound resonances in highly charged ions

TL;DR

This paper develops a level-resolved statistical theory for electron capture into complex, chaotic resonances in highly charged ions, improving understanding of recombination rates beyond previous models.

Contribution

It introduces a new statistical approach considering angular momentum and spectator electrons, applied to tungsten ions, with results aligning with earlier theories.

Findings

Recombination rates are significantly enhanced by compound resonances.

Spectator electrons have strong effects but do not alter the main theoretical conclusions.

The theory's predictions agree with experimental fluorescence yields.

Abstract

The strong mixing of many-electron basis states in excited atoms and ions with open $f$ shells results in very large numbers of complex, chaotic eigenstates that cannot be computed to any degree of accuracy. Describing the processes which involve such states requires the use of a statistical theory. Electron capture into these 'compound resonances' leads to electron-ion recombination rates that are orders of magnitude greater than those of direct, radiative recombination, and cannot be described by standard theories of dielectronic recombination. Previous statistical theories considered this as a two-electron capture process which populates a pair of single-particle orbitals, followed by 'spreading' of the two-electron states into chaotically mixed eigenstates. This method is similar to a configuration-average approach, as it neglects potentially important effects of spectator electrons and conservation of total angular momentum. In this work we develop a statistical theory which considers electron capture into 'doorway' states with definite angular momentum obtained by the configuration interaction method. We apply this approach to electron recombination with W$^{20+}$, considering 2 million doorway states. Despite strong effects from the spectator electrons, we find that the results of the earlier theories largely hold. Finally, we extract the fluorescence yield (the probability of photoemission and hence recombination) by comparison with experiment.