Critical densities

Critical densities - Critical densities. Decays from such

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Critical densities . Decays from such collisionally-excited transitions are usually forbidden (except for some strong UV carbon and Mg lines). The cooling rate is then L c = N e N i q 12 h ν 21 if the atoms remain in the excited state until they radiate. This is true as long as the density is much less than the critical density at which collisional de-excitation happens as often as radiation. This is a useful diagnostic - if we don't see certain lines of an ion, it may be because the density is too high for their radiation to occur. This happens when the mean time between collisions is comparable to or less than the radiative lifetime A 21 -1 . The critical density for a given transition is, by definition, that for which these rates are equal; note that we need to include all collisions that will change the electron's state. Per unit volume, at the critical density N cr , or using the q notation This may usually be calculated for a temperature 10 4 K (nebulae range from about 0.8 to 1.3
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Critical densities - Critical densities. Decays from such

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