Forbidden mechanism

In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of light by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particular selection rule but is allowed if the approximation associated with that rule is not made. For example, in a situation where, according to usual approximations (such as the electric-dipole approximation for the interaction with light), the process cannot happen, but at a higher level of approximation (e.g. magnetic dipole, or electric quadrupole) the process is allowed but at a much lower rate. In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of light by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particular selection rule but is allowed if the approximation associated with that rule is not made. For example, in a situation where, according to usual approximations (such as the electric-dipole approximation for the interaction with light), the process cannot happen, but at a higher level of approximation (e.g. magnetic dipole, or electric quadrupole) the process is allowed but at a much lower rate. An example is phosphorescent glow in the dark materials, which absorb light and form an excited state whose decay involves a spin flip, and is therefore forbidden by electric dipole transitions. The result is emission of light slowly over minutes or hours. Although the transitions are nominally forbidden, there is a small probability of their spontaneous occurrence, should an atomic nucleus, atom or molecule be raised to an excited state. More precisely, there is a certain probability that such an excited entity 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 or allowed 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 before any transition occurs via a forbidden route. Nevertheless, most forbidden transitions are only relatively unlikely: states that can only decay in this way (so-called meta-stable states) usually have lifetimes on the order milliseconds to seconds, compared to less than a microsecond for decay via permitted transitions. In some radioactive decay systems, multiple levels of forbiddenness can stretch life times by many orders of magnitude for each additional unit by which the system changes beyond what is most allowed under the selection rules. Such excited states can last years, or even for many billions of years (too long to have been measured). 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 ℏ {displaystyle hbar } of spin angular momentum. Such a change is necessary to emit a gamma-ray photon, which has a spin of 1 unit in this system. Integral changes of 2, 3, 4, and more units in angular momentum are possible (the emitted photons carry off the additional angular momentum), but changes of more than 1 unit are known as forbidden transitions. 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 highest known spin change of 8 units occurs in the decay of Ta-180m, which suppresses its decay by a factor of 1035 from that associated with 1 unit, so that instead of a natural gamma decay half life of 10−12 seconds, it has a half life of more than 1023 seconds, or at least 3 x 1015 years, and thus has yet to be observed to decay. Although gamma decays with nuclear angular momentum changes of 2, 3, 4, etc., are forbidden, they are only relatively forbidden, and do proceed, but with a slower rate than the normal allowed change of 1 unit. However, gamma emission is absolutely forbidden when the nucleus begins in a zero-spin state, as such an emission would not conserve angular momentum. These transitions cannot occur by gamma decay, but must proceed by another route, such as beta decay in some cases, or internal conversion where beta decay is not favored. Beta decay is classified according to the L-value of the emitted radiation. Unlike gamma decay, beta decay may proceed from a nucleus with a spin of zero and even parity to a nucleus also with a spin of zero and even parity (Fermi transition). This is possible because the electron and neutrino emitted may be of opposing spin (giving a radiation total angular momentum of zero), thus preserving angular momentum of the initial state even if the nucleus remains at spin-zero before and after emission. This type of emission is super-allowed meaning that it is the most rapid type of beta decay in nuclei that are susceptible to a change in proton/neutron ratios that accompanies a beta decay process. The next possible total angular momentum of the electron and neutrino emitted in beta decay is a combined spin of 1 (electron and neutrino spinning in the same direction), and is allowed. This 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 L > 0 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 (J) and parity (π). The selection rules for the Lth forbidden transitions are where Δπ = 1 or −1 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 ΔJ and Δπ values for the first few values of L: