  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.
