Atomic-physics calculations of radiative cooling are used to develop criteria for the overstability of radiating shocks. Our calculations explain the measurement of shock overstability by Grun et al. [Phys. Rev. Lett. 66, 2738 (1991)]] and explain why the overstability was not observed in other experiments. The methodology described here can be especially useful in astrophysical situations where the relevant properties leading to an overstability can be measured spectroscopically, but the effective adiabatic index is harder to determine.
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