Forbidden mechanism

A forbidden mechanism or forbidden line is a concept in physics/chemistry. It is a spectral line emitted by atoms undergoing energy transitions not normally allowed by the selection rules of quantum mechanics. In chemistry, "forbidden" means absolutely impossible due to natural laws, but with the assumption of an ideal symmetry. In physics it means that the process cannot proceed via the most efficient (electric dipole) route. Although the transitions are nominally "forbidden", there is a non-zero probability of their spontaneous occurrence, should an atom or molecule be raised to an excited state. More precisely, there is a certain probability that such an excited atom will make a forbidden transition to a lower energy state per unit time; by definition this probability is much lower than that for any transition permitted by the selection rules. Therefore, if a state can de-excite via a permitted transition (or otherwise, e.g. via collisions) it will almost certainly do so rather than choosing the forbidden route. Nevertheless, "forbidden" transitions are only relatively unlikely: states that can only decay in this way (so-called meta-stable states) usually have lifetimes of order milliseconds to seconds, compared to less than a microsecond for decay via permitted transitions.

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, once an atom or molecule has been excited for any reason into a meta-stable state, then it is almost certain to decay by emitting a forbidden-line photon. Since meta-stable states are rather common, forbidden transitions account for a significant percentage of the photons emitted by the ultra-low density gas in space.

Forbidden line transitions are noted by placing square brackets around the atomic or molecular species in question, e.g. [OIII] 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. Also, the forbidden 21-cm hydrogen line is of the utmost importance for radio astronomy as it allows very cold neutral hydrogen gas to be seen.

References

• Osterbrock, D.E., Astrophysics of gaseous nebulae and active galactic nuclei, University Science Books, 1989, ISBN 0-935702-22-9.