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.
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