# Selection rule

Selection rule

In physics and chemistry, especially in the context of quantum mechanics, a selection rule is a condition constraining the physical properties of the initial system and the final system that is necessary for a process to occur with a nonzero probability.clarifyme

In many cases, a transition involves the emission of radiation, that is, a photon is emitted.In general, electric (charge) radiation or magnetic (current, magnetic moment radiation) can be classified into multipoles Eλ (electric) or Mλ (magnetic) of order 2λ, e.g. E1 for electric dipole, E2 for quadrupole, or E3 for octupole. In transitions where the change in angular momentum between the initial and final states makes a several multipole radiations possible, usually the lowest order multipoles are overwhelmingly more likely, and dominate the transition.

The emitted particle carries away an angular momentum λ, which for the photon must be at least 1, since it is a vector particle (i.e., it has "J""P" = 1). Thus there is no E0 (electric monopoles) or M0 (magnetic monopoles) radiation (the latter is forbidden because magnetic monopoles do not seem to exist).

Since the total angular momentum has to be conserved during the transition, we have that:where , and its z-projection is given by $lambda_z = mu , hbar.$ The corresponding quantum numbers "λ", "μ" must satisfy:$| J_\left\{mathrm\left\{i - J_\left\{mathrm\left\{f | le lambda le J_\left\{mathrm\left\{i + J_\left\{mathrm\left\{f$and:$mu = M_\left\{mbox\left\{i - M_\left\{mbox\left\{f,.$

Parity is also preserved. For electric multipole transitions :$pi\left(mathrm\left\{E\right\}lambda\right) = pi_\left\{mathrm\left\{i pi_\left\{mathrm\left\{f = \left(-1\right)^\left\{lambda\right\},$while for magnetic multipoles:$pi\left(mathrm\left\{M\right\}lambda\right) = pi_\left\{mathrm\left\{i pi_\left\{mathrm\left\{f = \left(-1\right)^\left\{lambda+1\right\},.$Thus, parity does not change for E-even or M-odd multipoles, while it changes for E-odd or M-even multipoles.

These considerations generate different sets of transitions rules depending on the multipole order and type. The expression "forbidden transitions" is often used; this does not mean that these transitions cannot occur, only that they are "electric-dipole forbidden". These transitions are perfectly possible, they merely occur at a lower rate. If the rate for an E1 transition is non-zero, the transition is said to be permitted; if it is zero, then M1, E2, etc. transitions can still produce radiation, albeit with much lower transitions rates. These are the so-called forbidden transitions. The transition rate decreases by a factor of approximately 10−3 from one multipole to the next one, so the lowest multipole transitions are most likely to occur.

Semi-forbidden transitions (resulting in so called intercombination lines) are electric dipole (E1) transitions for which the selection rule that the spin does not change is violated. This is a result of the failure of LS coupling.

ummary table

* [http://physics.nist.gov/Pubs/AtSpec/node17.html National Institute of Standards and Technology]
* [http://www.shef.ac.uk/physics/teaching/phy332/atomic_physics3.pdf Lecture notes from The University of Sheffield]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• selection rule — Physics. any of several rules designating allowed transitions between quantum states in terms of the quantum numbers associated with the states. * * * ▪ atomic physics       in quantum mechanics, any of a set of restrictions governing the… …   Universalium

• selection rule — atrankos taisyklė statusas T sritis fizika atitikmenys: angl. selection rule vok. Auswahlregel, f rus. правило отбора, n pranc. loi de sélection, f; règle de sélection, f …   Fizikos terminų žodynas

• selection rule — atrankos taisyklė statusas T sritis Standartizacija ir metrologija apibrėžtis Taisyklė, nusakanti kvantinių vyksmų tikimybę. atitikmenys: angl. selection rule vok. Auswahlregel, f rus. правило отбора, n pranc. règle de sélection, f …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

• selection rule — atrankos taisyklė statusas T sritis chemija apibrėžtis Taisyklė, nusakanti kvantinių procesų tikimybę. atitikmenys: angl. selection rule rus. правило отбора …   Chemijos terminų aiškinamasis žodynas

• selection rule — noun Physics a rule which describes whether particular quantum transitions in an atom or molecule are allowed or forbidden …   English new terms dictionary

• selection rule — noun : a rule that states which of all the conceivable changes in the state of a quantized system (atoms, nuclei, or related entities) are physically possible under specified circumstances usually in terms of the possible numerical changes in the …   Useful english dictionary

• selection rule — noun Any of several general rules concerning the transitions between the states of a quantum mechanical system; they derive from the symmetry properties of the states and of their interactions …   Wiktionary

• forbiddenness due to a selection rule — atrankinis draudimas statusas T sritis fizika atitikmenys: angl. forbiddenness due to a selection rule vok. Auswahlverbot, n rus. запрет вследствие правила отбора, m pranc. interdiction due à la règle de sélection, f …   Fizikos terminų žodynas

• Surface selection rule — In surface vibrational spectroscopy, the surface selection rule is applied to identify the peaks observed in vibrational spectra. When a molecule is adsorbed on a substrate, the molecule induces opposite image charges in the substrate. The dipole …   Wikipedia

• Rule 5 draft — The Rule 5 draft is a Major League Baseball player draft that occurs each year in December, at the annual Winter Meeting of general managers. The Rule 5 draft aims to prevent teams from stockpiling too many young players on their minor league… …   Wikipedia