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We examine the Sastry (athermal cavitation) transitions for model monatomic liquids interacting via Lennard-Jones as well as shorter- and longer-ranged pair potentials. Low-temperature thermodynamically stable liquids have $ρ< ρ_S$ except when the attractive forces are long-ranged. For moderate- and short-ranged attractions, stable liquids with $ρ> ρ_S$ exist at higher temperatures; the pressures in these liquids are high, but the Sastry transition may strongly influence their cavitation under dynamic hydrostatic expansion. The temperature $T^*$ at which stable $ρ> ρ_S$ liquids emerge is $\sim 0.84ε/k_B$ for Lennard-Jones liquids; $T^*$ decreases (increases) rapidly with increasing (decreasing) pair-interaction range. In particular, for short-ranged potentials, $T^*$ is above the critical temperature. All liquids' inherent structures are isostructural (isomorphic) for densities below (above) the Sastry density $ρ_S$. Overall, our results suggest that the barriers to cavitation in most simple liquids under ambient conditions where significant cavitation is likely to occur are primarily vibrational-energetic and entropic rather than configurational-energetic. The most likely exceptions to this rule are liquids with long-ranged pair interactions, such as alkali metals. The most likely exceptions to this rule are liquids with long-ranged pair interactions, such as alkali metals.