  Low spectral resolution (delta lambda/lambda ~ 50) mid-infrared observations
with high angular resolution (0.3--0.5'') using the Long Wavelength
Spectrometer on the Keck I Telescope are reported of the nuclei of five highly
luminous infrared bright galaxies. Spectra of eight distinct nuclei, ranging in
luminosity from 10^11 L_sun to >10^12 L_sun have been obtained. Four of the
nuclei show the characteristic PAH emission features, i.e. 11.3 micron emission
as well as the 8.6 micron shoulder of the 7.7 micron band. The other nuclei
show either weak PAH emission bands or no evidence for these bands. The high
spatial resolution of the observations reveals extended emission in the 11.3
micron PAH band associated with several of the compact nuclear sources. When
proper account is taken of the diffuse PAH emission, most of the compact
sources show little or no directly associated PAH emission. The diffuse PAH
emission is extended over spatial scales of 100--500 pc; its presence shows
that there is significant circumnuclear UV/optical emission exciting the
aromatic bands, most likely associated with circumnuclear starbursts. After the
spectra of the nuclear sources are corrected for the spectrum of the diffuse
PAH emission, the peak apparent silicate optical depth at 9.7 microns can be as
great as 15, corresponding to > 150 magnitudes of visible light extinction.
Because of the large silicate optical depths, mid-infrared spectra are not
probing the nature of the true nuclei in the most opaque compact sources.
