  We have carried-out a series of multi-configuration Breit-Pauli AUTOSTRUCTURE
calculations for the dielectronic recombination of Fe^{13+}. We present a
detailed comparison of the results with the high-energy resolution measurements
reported recently from the Heidelberg Test Storage Ring by Schmidt et al. Many
Rydberg series contribute significantly from this initial 3s^2 3p M-shell ion,
resulting in a complex recombination `spectrum'. While there is much close
agreement between theory and experiment, differences of typically 50% in the
summed resonance strengths over 0.1-10 eV result in the experimentally based
total Maxwellian recombination rate coefficient being a factor of 1.52-1.38
larger than theory over 10^4-10^5 K, which is a typical temperature range of
peak abundance for Fe^{13+} in a photoionized plasma. Nevertheless, this
theoretical recombination rate coefficient is an order of magnitude larger than
that used by modellers to-date. This may help explain the discrepancy between
the iron M-shell ionization balance predicted by photoionization modelling
codes such as ION and CLOUDY and that deduced from the iron M-shell
unresolved-transition-array absorption feature observed in the X-ray spectrum
of many active galactic nuclei. Similar data are required for Fe^{8+} through
Fe^{12+} to remove the question mark hanging over the atomic data though.
