  We present the data and our analysis of MIR fine-structure emission lines
detected in Spitzer/IRS high-res spectra of 202 local LIRGs observed as part of
the GOALS project. We detect emission lines of [SIV], [NeII], [NeV], [NeIII],
[SIII]18.7, [OIV], [FeII], [SIII]33.5, and [SiII]. Over 75% of our galaxies are
classified as starburst (SB) sources in the MIR. We compare ratios of the
emission line fluxes to stellar photo- and shock-ionization models to constrain
the gas properties in the SB nuclei. Comparing the [SIV]/[NeII] and
[NeIII]/[NeII] ratios to the Starburst99-Mappings III models with an
instantaneous burst history, the line ratios suggest that the SB in our LIRGs
have ages of 1-4.5Myr, metallicities of 1-2Z_sun, and ionization parameters of
2-8e7cm/s. Based on the [SIII]/[SIII] ratios, the electron density in LIRG
nuclei has a median electron density of ~300cm-3 for sources above the low
density limit. We also find that strong shocks are likely present in 10 SB
sources. A significant fraction of the GOALS sources have resolved neon lines
and 5 show velocity differences of >200km/s in [NeIII] or [NeV] relative to
[NeII]. Furthermore, 6 SB and 5 AGN LIRGs show a trend of increasing line width
with ionization potential, suggesting the possibility of a compact energy
source and stratified ISM in their nuclei. We confirm a strong correlation
between the [NeII]+[NeIII] emission, as well as [SIII]33.5, with both the IR
luminosity and the 24um warm dust emission measured from the spectra. Finally,
we find no correlation between the hardness of the radiation field or the line
width and the ratio of the total IR to 8um emission (IR8). This may be because
the IR luminosity and the MIR fine-structure lines are sensitive to different
timescales over the SB, or that IR8 is more sensitive to the geometry of the
warm dust region than the radiation field producing the HII region emission.
