  We present infrared 2.8-4.1 micron slit spectra of 32 Seyfert 2 galaxies in
the CfA and 12 micron samples. The 3.3 micron polycyclic aromatic hydrocarbon
(PAH) emission feature was used to estimate the absolute magnitude of a compact
nuclear starburst (< a few 100 pc in size) that is presumed to have occurred in
the outer region of an obscuring dusty molecular torus around a central
supermassive black hole. We detected 3.3 micron PAH emission in 11 of the 32
Seyfert 2 nuclei in our sample, providing evidence for the presence of compact
nuclear starbursts in a significant fraction of Seyfert 2 nuclei. However, the
rest-frame equivalent widths of the 3.3 micron PAH emission, and the 3.3 micron
PAH-to-infrared luminosity ratios measured in this study suggest that compact
nuclear starbursts generally do not contribute significantly to the observed
3-4 micron nuclear fluxes or to the infrared luminosities of Seyfert 2
galaxies. Small optical depths of absorption features at 3.4 micron from bare
dust and at 3.1 micron from ice-covered dust suggest that dust extinction
toward the 3-4 micron continuum-emitting region in the innermost part of the
obscuring dusty torus is modest: AV < 50-60 mag. Finally, the 3.3 micron PAH
emission luminosities measured in this study were found to be significantly
correlated with IRAS 12- and 25-micron, and nuclear N-band (10.6 micron)
luminosities. If these three luminosities trace the power of the active
galactic nucleus (AGN), then the luminosities of compact nuclear starbursts and
AGNs are correlated. This correlation is in agreement with theories predicting
that the presence of a compact nuclear starburst in the torus leads to an
enhancement of the mass accretion rate onto the central supermassive black
hole.
