We present mid-infrared spectroscopy of the prototypical interacting g
alaxies NGC 4038/39 (the 'Antennae') obtained with the ISO Short Wavel
ength Spectrometer (SWS). Our observations focus on the interaction zo
ne where the two galaxies overlap, providing new constraints on the pr
operties of the young and vigorous extranuclear starburst triggered by
the recent interaction of the two galaxies. We use hydrogen recombina
tion lines to derive an extinction of A(v) approximate to 70 to the st
arburst region, concluding that a model where emitting gas and absorbi
ng dust are mixed best fits the data. We discuss the use of mid-infrar
ed fine structure line ratios for determining the average effective te
mperature of the stellar ionizing radiation field, and derive an avera
ge temperature of 44000 K from the extinction-corrected [NeIII]15.6 mu
m/[NeII]12.8 mu m line ratio. The observations are well described by
starburst models for a recent starburst with an initial mass function
extending up to 100 Mg.. Observations of the pure rotational (0-0) S(1
) and S(2) lines of molecular hydrogen are used to constrain the fract
ion of molecular gas that is at temperatures of a few hundred Kelvin.