We have measured resonance strengths and energies for dielectronic
recombination (DR) of Mg-like Fe XV forming Al-like Fe XIV via N=3 -> N' = 3
core excitations in the electron-ion collision energy range 0-45 eV. All
measurements were carried out using the heavy-ion Test Storage Ring at the Max
Planck Institute for Nuclear Physics in Heidelberg, Germany. We have also
carried out new multiconfiguration Breit-Pauli (MCBP) calculations using the
AUTOSTRUCTURE code. For electron-ion collision energies < 25 eV we find poor
agreement between our experimental and theoretical resonance energies and
strengths. From 25 to 42 eV we find good agreement between the two for
resonance energies. But in this energy range the theoretical resonance
strengths are ~ 31% larger than the experimental results. This is larger than
our estimated total experimental uncertainty in this energy range of +/- 26%
(at a 90% confidence level). Above 42 eV the difference in the shape between
the calculated and measured 3s3p(^1P_1)nl DR series limit we attribute partly
to the nl dependence of the detection probabilities of high Rydberg states in
the experiment. We have used our measurements, supplemented by our
AUTOSTRUCTURE calculations, to produce a Maxwellian-averaged 3 -> 3 DR rate
coefficient for Fe XV forming Fe XIV. The resulting rate coefficient is
estimated to be accurate to better than +/- 29% (at a 90% confidence level) for
k_BT_e > 1 eV. At temperatures of k_BT_e ~ 2.5-15 eV, where Fe XV is predicted
to form in photoionized plasmas, significant discrepancies are found between
our experimentally-derived rate coefficient and previously published
theoretical results. Our new MCBP plasma rate coefficient is 19-28% smaller
than our experimental results over this temperature range