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

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