An example is phosphorescent glow-in-the-dark materials,[2] which absorb light and form an excited state whose decay involves a spin flip, and is therefore forbidden by electric dipole transitions.
The most common mechanism for suppression of the rate of gamma decay of excited atomic nuclei, and thus make possible the existence of a metastable isomer for the nucleus, is lack of a decay route for the excited state that will change nuclear angular momentum (along any given direction) by the most common (allowed) amount of 1 quantum unit
Each degree of forbiddenness (additional unit of spin change larger than 1, that the emitted gamma ray must carry) inhibits decay rate by about 5 orders of magnitude.
The following table lists the ΔJ and Δπ values for the first few values of L: 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.
[5] Geochemical experiments have also found this rare type of forbidden decay in several isotopes,[6] with mean half lives over 1018 yr.
Forbidden transitions in rare earth atoms such as erbium and neodymium make them useful as dopants for solid-state lasing media.
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.
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 transitions in highly charged ions resulting in the emission of visible, vacuum-ultraviolet, soft x-ray and x-ray photons are routinely observed in certain laboratory devices such as electron beam ion traps [9] and ion storage rings, where in both cases residual gas densities are sufficiently low for forbidden line emission to occur before atoms are collisionally de-excited.
Also, the presence of [O I] and [S II] forbidden lines in the spectra of T-tauri stars implies low gas density.
Forbidden line transitions are noted by placing square brackets around the atomic or molecular species in question, e.g. [O III] or [S II].