A forbidden line is a spectral line emitted by atoms undergoing energy transitions not normally allowed by the selection rules of quantum mechanics. Although they are technically forbidden, there is a non-zero probability of their spontaneous occurrence, should an atom or molecule be raised to an excited state. The transition probability is extremely low, however, so if the atom or molecule can make an allowed transition or be otherwise de-excited to a lower energy state, it will almost certainly do so.
Forbidden emission lines have only been observed in extremely low-density gases and plasmas, either in outer space or in the extreme upper atmosphere of the Earth. Even the hardest laboratory vacuum on Earth is still too dense for forbidden line emission to occur before atoms are collisionally de-excited. However, in space environments, densities may be only a few atoms per cubic centimetre, making atomic collisions unlikely. Under such conditions, forbidden line transitions may account for a significant percentage of the photons emitted.
Forbidden line transitions are noted by placing square brackets around the atomic or molecular species in question, e.g. [O III] or [S II]. Forbidden lines of nitrogen ([N II] at 654.8 and 658.4 nm), sulfur ([S II] at 671.6 and 673.1 nm), and oxygen ([O II] at 372.7 nm, and [O III] at 495.9 and 500.7 nm) are commonly observed in astrophysical plasmas. These lines are extremely important to the energy balance of such things as planetary nebulae and H II regions.
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