  An exclusive measurement of the decay eta --> pi+ pi- gamma has been
performed at the WASA facility at COSY. The eta mesons were produced in the
fusion reaction pd --> 3He X at a proton beam momentum of 1.7 GeV/c. Efficiency
corrected differential distributions have been extracted based on 13340\pm140
events after background subtraction. The measured pion angular distribution is
consistent with a relative p-wave of the two-pion system, whereas the measured
photon energy spectrum was found at variance with the simplest gauge invariant
matrix element of eta --> pi+ pi- gamma. A parameterization of the data can be
achieved by the additional inclusion of the empirical pion vector form factor
multiplied by a first-order polynomial in the squared invariant mass of the pi+
pi- system.
