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The optically thin critical densities and the effective excitation densitiesto produce a 1 K km/s (or 0.818 Jy km/s $(\frac{\nu_{jk}}{100 \rm{GHz}})^2 \,(\frac{\theta_{beam}}{10^{\prime\prime}})^2$) spectral line are tabulated for12 commonly observed dense gas molecular tracers. The dependence of thecritical density and effective excitation density on physical assumptions (i.e.gas kinetic temperature and molecular column density) is analyzed. Criticaldensities for commonly observed dense gas transitions in molecular clouds (i.e.HCN $1-0$, HCO$^+$ $1-0$, N$_2$H$^+$ $1-0$) are typically $1 - 2$ orders ofmagnitude larger than effective excitation densities because the standarddefinitions of critical density do not account for radiative trapping and 1 Kkm/s lines are typically produced when radiative rates out of the upper energylevel of the transition are faster than collisional depopulation. The use ofeffective excitation density has a distinct advantage over the use of criticaldensity in characterizing the differences in density traced by species such asNH$_3$, HCO$^+$, N$_2$H$^+$, and HCN as well as their isotpologues; but, theeffective excitation density has the disadvantage that it is undefined fortransitions when $E_u/k \gg T_k$, for low molecular column densities, and forheavy molecules with complex spectra (i.e. CH$_3$CHO).

The Critical Density and the Effective Excitation Density of Commonly Observed Molecular Dense Gas Tracers