type of emission (Gamow-Teller transition) changes nuclear spin by 1 to compensate. States involving higher angular momenta of the emitted radiation (2, 3, 4, etc.) are forbidden and are ranked in degree of forbiddenness by their increasing angular momentum. Specifically, when the decay is referred to as forbidden. Nuclear selection rules require L-values greater than two to be accompanied by changes in both nuclear spin () and parity (π). The selection rules for the th forbidden transitions are where or corresponds to no parity change or parity change, respectively. As noted, the special case of a Fermi 0+ → 0+ transition (which in gamma decay is absolutely forbidden) is referred to as super-allowed for beta decay, and proceeds very quickly if beta decay is possible. The following table lists the Δ and Δπ values for the first few values of : As with gamma decay, each degree of increasing forbiddenness increases the half life of the beta decay process involved by a factor of about 4 to 5 orders of magnitude. Double beta decay has been observed in the laboratory, e.g. in . Geochemical experiments have also found this rare type of forbidden decay in several isotopes. with mean half lives over 1018 yr . In solid-state physics Forbidden transitions in rare earth atoms such as erbium and neodymium make them useful as dopants for solid-state lasing media. In such media, the atoms are held in a matrix which keeps them from de-exciting by collision, and the long half life of their excited states makes them easy to optically pump to create a large population of excited atoms. Neodymium doped glass derives its unusual coloration from forbidden f-f transitions within the neodymium atom, and is used in extremely high power solid state lasers. Bulk semiconductor transitions can also be forbidden by symmetry, which change the functional form of the absorption spectrum, as can be shown in a Tauc plot. In astrophysics and atomic physics Forbidden emission lines have been observed in extremely low-density gases and plasmas, either in outer space or in the extreme upper atmosphere of the Earth. 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