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class="mw-page-title-main">Forbidden mechanism</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://ca.wikipedia.org/wiki/L%C3%ADnia_prohibida" title="Línia prohibida – Catalan" lang="ca" hreflang="ca" data-title="Línia prohibida" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Verbotener_%C3%9Cbergang" title="Verbotener Übergang – German" lang="de" hreflang="de" data-title="Verbotener Übergang" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/L%C3%ADnea_prohibida" title="Línea prohibida – Spanish" lang="es" hreflang="es" data-title="Línea prohibida" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Raie_de_transition_interdite" title="Raie de transition interdite – French" lang="fr" hreflang="fr" data-title="Raie de transition interdite" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%88%EC%A7%80%EC%84%A0" title="금지선 – Korean" lang="ko" hreflang="ko" data-title="금지선" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Zabranjene_crte" title="Zabranjene crte – Croatian" lang="hr" hreflang="hr" data-title="Zabranjene crte" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link 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data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Forbidden Lines" redirects here. For the 2004 Indian film, see <a href="/wiki/Lakeer_%E2%80%93_Forbidden_Lines" title="Lakeer – Forbidden Lines">Lakeer – Forbidden Lines</a>.</div> <p>In <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscopy</a>, a <b>forbidden mechanism</b> (<b>forbidden transition</b> or <b>forbidden line</b>) is a <a href="/wiki/Spectral_line" title="Spectral line">spectral line</a> associated with absorption or emission of photons by <a href="/wiki/Atomic_nuclei" class="mw-redirect" title="Atomic nuclei">atomic nuclei</a>, <a href="/wiki/Atom" title="Atom">atoms</a>, or <a href="/wiki/Molecule" title="Molecule">molecules</a> which undergo a transition that is not allowed by a particular <a href="/wiki/Selection_rule" title="Selection rule">selection rule</a> but is allowed if the approximation associated with that rule is not made.<sup id="cite_ref-BunkerJensen2006_1-0" class="reference"><a href="#cite_note-BunkerJensen2006-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> For example, in a situation where, according to usual approximations (such as the <a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">electric dipole approximation</a> for the interaction with light), the process cannot happen, but at a higher level of approximation (e.g. <a href="/wiki/Magnetic_dipole_moment" class="mw-redirect" title="Magnetic dipole moment">magnetic dipole</a>, or electric <a href="/wiki/Quadrupole" title="Quadrupole">quadrupole</a>) the process is allowed but at a low rate. </p><p>An example is <a href="/wiki/Phosphorescence" title="Phosphorescence">phosphorescent</a> glow-in-the-dark materials,<sup id="cite_ref-LisenskyPatel1996_2-0" class="reference"><a href="#cite_note-LisenskyPatel1996-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> which absorb light and form an excited state whose decay involves a <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> flip, and is therefore forbidden by electric dipole transitions. The result is emission of light slowly over minutes or hours. </p><p>Should an <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a>, <a href="/wiki/Atom" title="Atom">atom</a> or <a href="/wiki/Molecule" title="Molecule">molecule</a> be raised to an excited state and should the transitions be nominally forbidden, then there is still a small probability of their spontaneous occurrence. 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 <a href="/wiki/Metastability" title="Metastability">meta-stable</a> 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.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2015)">citation needed</span></a></i>]</sup> Such excited states can last years, or even for many billions of years (too long to have been measured). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="In_radioactive_decay">In radioactive decay</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=1" title="Edit section: In radioactive decay"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Gamma_decay">Gamma decay</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=2" title="Edit section: Gamma decay"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The most common mechanism for suppression of the rate of gamma decay of excited atomic nuclei, and thus make possible the existence of a <a href="/wiki/Metastable_isomer" class="mw-redirect" title="Metastable isomer">metastable isomer</a> 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 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span> of <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a>. 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.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The highest known spin change of 8 units occurs in the decay of <a href="/wiki/Isotopes_of_tantalum" title="Isotopes of tantalum">Ta-180m</a>, which suppresses its decay by a factor of 10<sup>35</sup> from that associated with 1 unit, so that instead of a natural gamma decay half life of 10<sup>−12</sup> seconds, it has a half life of more than 10<sup>23</sup> seconds, or at least 3 x 10<sup>15</sup> years, and thus has yet to be observed to decay. </p><p>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 and ends 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 <a href="/wiki/Beta_decay" title="Beta decay">beta decay</a> in some cases, or <a href="/wiki/Internal_conversion" title="Internal conversion">internal conversion</a> where beta decay is not favored. </p> <div class="mw-heading mw-heading3"><h3 id="Beta_decay">Beta decay</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=3" title="Edit section: Beta decay"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Beta decay is classified according to the <a href="/wiki/Angular_momentum_operator" title="Angular momentum operator"><span class="texhtml mvar" style="font-style:italic;">L</span>-value</a> 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. </p><p>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 (<a href="/wiki/Gamow-Teller_transition" class="mw-redirect" title="Gamow-Teller transition">Gamow-Teller transition</a>) 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. </p><p>Specifically, when <span class="texhtml"><i>L</i> > 0</span> the decay is referred to as forbidden. Nuclear <a href="/wiki/Selection_rules" class="mw-redirect" title="Selection rules">selection rules</a> require L-values greater than two to be accompanied by changes in both <a href="/wiki/Nuclear_spin" class="mw-redirect" title="Nuclear spin">nuclear spin</a> (<span class="texhtml mvar" style="font-style:italic;">J</span>) and <a href="/wiki/Parity_(physics)" title="Parity (physics)">parity</a> (π). The selection rules for the <span class="texhtml mvar" style="font-style:italic;">L</span>th forbidden transitions are </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>J</mi> <mo>=</mo> <mi>L</mi> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mi>L</mi> <mo>,</mo> <mi>L</mi> <mo>+</mo> <mn>1</mn> <mo>;</mo> <mi mathvariant="normal">Δ</mi> <mi>π</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/079c6ef49f11faa38b1a2630e6563f4ecb0a942e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.506ex; height:3.176ex;" alt="{\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}"></span> </p><p>where <span class="texhtml">Δπ = 1</span> or <span class="texhtml">−1</span> corresponds to no parity change or parity change, respectively. As noted, the special case of a Fermi 0<sup>+</sup> → 0<sup>+</sup> 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<span class="texhtml mvar" style="font-style:italic;">J</span> and Δπ values for the first few values of <span class="texhtml mvar" style="font-style:italic;">L</span>: </p> <table class="wikitable"> <tbody><tr> <th>Forbiddenness</th> <th>Δ<span class="texhtml mvar" style="font-style:italic;">J</span></th> <th>Δπ </th></tr> <tr> <td>Superallowed</td> <td>0<sup>+</sup> → 0<sup>+</sup></td> <td>no </td></tr> <tr> <td>Allowed</td> <td>0, 1</td> <td>no </td></tr> <tr> <td>First forbidden</td> <td>0, 1, 2</td> <td>yes </td></tr> <tr> <td>Second forbidden</td> <td>1, 2, 3</td> <td>no </td></tr> <tr> <td>Third forbidden</td> <td>2, 3, 4</td> <td>yes </td></tr></tbody></table> <p>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.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Double_beta_decay" title="Double beta decay">Double beta decay</a> has been observed in the laboratory, e.g. in <span style="white-space:nowrap;"><a href="/wiki/Selenium-82" class="mw-redirect" title="Selenium-82"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">82</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>Se<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></a></span>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Geochemical experiments have also found this rare type of forbidden decay in several isotopes,<sup id="cite_ref-Barabash2011_6-0" class="reference"><a href="#cite_note-Barabash2011-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> with mean half lives over 10<sup>18</sup> yr. </p> <div class="mw-heading mw-heading2"><h2 id="In_solid-state_physics">In solid-state physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=4" title="Edit section: In solid-state physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Forbidden_mechanism" title="Special:EditPage/Forbidden mechanism">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">October 2023</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Forbidden transitions in rare earth atoms such as <a href="/wiki/Erbium" title="Erbium">erbium</a> and <a href="/wiki/Neodymium" title="Neodymium">neodymium</a> make them useful as <a href="/wiki/Dopants" class="mw-redirect" title="Dopants">dopants</a> for solid-state lasing media.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> 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 <i>f</i>-<i>f</i> transitions within the neodymium atom, and is used in extremely high power <a href="/wiki/Solid_state_laser" class="mw-redirect" title="Solid state laser">solid state lasers</a>. Bulk <a href="/wiki/Semiconductor" title="Semiconductor">semiconductor</a> transitions can also be forbidden by symmetry, which change the functional form of the absorption spectrum, as can be shown in a <a href="/wiki/Tauc_plot" title="Tauc plot">Tauc plot</a>. </p> <div class="mw-heading mw-heading2"><h2 id="In_astrophysics_and_atomic_physics">In astrophysics and atomic physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=5" title="Edit section: In astrophysics and atomic physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Forbidden emission lines have been observed in extremely low-<a href="/wiki/Density" title="Density">density</a> gases and <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasmas</a>, either in <a href="/wiki/Outer_space" title="Outer space">outer space</a> or in the extreme <a href="/wiki/Upper_atmosphere" title="Upper atmosphere">upper atmosphere</a> of the <a href="/wiki/Earth" title="Earth">Earth</a>.<sup id="cite_ref-EDoA_161_8-0" class="reference"><a href="#cite_note-EDoA_161-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In space environments, densities may be only a few atoms per <a href="/wiki/Cubic_centimetre" title="Cubic centimetre">cubic centimetre</a>, 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 transitions in <a href="/wiki/Highly_charged_ion" title="Highly charged ion">highly charged ions</a> resulting in the emission of visible, <a href="/wiki/Ultraviolet#VUV" title="Ultraviolet">vacuum-ultraviolet</a>, soft x-ray and x-ray photons are routinely observed in certain laboratory devices such as <a href="/wiki/Electron_beam_ion_trap" title="Electron beam ion trap">electron beam ion traps</a> <sup id="cite_ref-Maeckel2011_9-0" class="reference"><a href="#cite_note-Maeckel2011-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and ion <a href="/wiki/Storage_ring" title="Storage ring">storage rings</a>, where in both cases residual gas densities are sufficiently low for forbidden line emission to occur before atoms are <a href="/wiki/Collision" title="Collision">collisionally</a> de-excited. Using <a href="/wiki/Laser_spectroscopy" class="mw-redirect" title="Laser spectroscopy">laser spectroscopy</a> techniques, forbidden transitions are used to stabilize <a href="/wiki/Atomic_clock" title="Atomic clock">atomic clocks</a> and <a href="/wiki/Quantum_clock" class="mw-redirect" title="Quantum clock">quantum clocks</a> that have the highest accuracies currently available. </p><p>Forbidden lines of <a href="/wiki/Nitrogen" title="Nitrogen">nitrogen</a> ([N II] at 654.8 and 658.4 <a href="/wiki/Nanometer" class="mw-redirect" title="Nanometer">nm</a>), <a href="/wiki/Sulfur" title="Sulfur">sulfur</a> ([S II] at 671.6 and 673.1 nm), and <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> ([O II] at 372.7 nm, and <a href="/wiki/Doubly_ionized_oxygen" title="Doubly ionized oxygen">[O III]</a> at 495.9 and 500.7 nm) are commonly observed in <a href="/wiki/Astrophysical_plasma" title="Astrophysical plasma">astrophysical plasmas</a>. These lines are important to the <a href="/wiki/Energy_economics" title="Energy economics">energy balance</a> of <a href="/wiki/Planetary_nebula" title="Planetary nebula">planetary nebulae</a> and <a href="/wiki/H_II_region" title="H II region">H II regions</a>. The forbidden <a href="/wiki/Hydrogen_line" title="Hydrogen line">21-cm hydrogen line</a> is particularly important for <a href="/wiki/Radio_astronomy" title="Radio astronomy">radio astronomy</a> as it allows very cold neutral hydrogen gas to be seen. Also, the presence of [O I] and [S II] forbidden lines in the spectra of T-tauri stars implies low gas density. </p> <div class="mw-heading mw-heading3"><h3 id="Notation">Notation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=6" title="Edit section: Notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Forbidden line transitions are noted by placing square brackets around the atomic or molecular species in question, e.g. [O III] or [S II].<sup id="cite_ref-EDoA_161_8-1" class="reference"><a href="#cite_note-EDoA_161-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-BunkerJensen2006-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-BunkerJensen2006_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFPhilip_R._BunkerPer_Jensen2006" class="citation book cs1">Philip R. 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Lviv: ЛНУ—ГАО НАНУ. p. 161. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/966-613-263-X" title="Special:BookSources/966-613-263-X"><bdi>966-613-263-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%D0%97%D0%B0%D0%B1%D0%BE%D1%80%D0%BE%D0%BD%D0%B5%D0%BD%D1%96+%D0%BB%D1%96%D0%BD%D1%96%D1%97&rft.btitle=%D0%90%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D1%96%D1%87%D0%BD%D0%B8%D0%B9+%D0%B5%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%87%D0%BD%D0%B8%D0%B9+%D1%81%D0%BB%D0%BE%D0%B2%D0%BD%D0%B8%D0%BA&rft.place=Lviv&rft.pages=161&rft.pub=%D0%9B%D0%9D%D0%A3%E2%80%94%D0%93%D0%90%D0%9E+%D0%9D%D0%90%D0%9D%D0%A3&rft.date=2003&rft.isbn=966-613-263-X&rft_id=http%3A%2F%2Fastro.lnu.edu.ua%2Fastro%2Fbukvy%2Fz1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForbidden+mechanism" class="Z3988"></span></span> </li> <li id="cite_note-Maeckel2011-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Maeckel2011_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMäckel,_V.Klawitter,_R.Brenner,_G.Crespo_López-Urrutia,_J._R.2011" class="citation journal cs1">Mäckel, V.; Klawitter, R.; Brenner, G.; Crespo López-Urrutia, J. R.; Ullrich, J. (2011). "Laser Spectroscopy on Forbidden Transitions in Trapped Highly Charged Ar<sup>13+</sup> Ions". <i>Physical Review Letters</i>. <b>107</b> (14). American Physical Society: 143002. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PhRvL.107n3002M">2011PhRvL.107n3002M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.107.143002">10.1103/PhysRevLett.107.143002</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22107188">22107188</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Laser+Spectroscopy+on+Forbidden+Transitions+in+Trapped+Highly+Charged+Ar%3Csup%3E13%2B%3C%2Fsup%3E+Ions&rft.volume=107&rft.issue=14&rft.pages=143002&rft.date=2011&rft_id=info%3Apmid%2F22107188&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.107.143002&rft_id=info%3Abibcode%2F2011PhRvL.107n3002M&rft.au=M%C3%A4ckel%2C+V.&rft.au=Klawitter%2C+R.&rft.au=Brenner%2C+G.&rft.au=Crespo+L%C3%B3pez-Urrutia%2C+J.+R.&rft.au=Ullrich%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForbidden+mechanism" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forbidden_mechanism&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><a href="/wiki/Donald_Edward_Osterbrock" title="Donald Edward Osterbrock">Osterbrock, D.E.</a>, <i>Astrophysics of gaseous nebulae and active galactic nuclei</i>, University Science Books, <a href="/wiki/1989_in_literature" title="1989 in literature">1989</a>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-935702-22-9" title="Special:BookSources/0-935702-22-9">0-935702-22-9</a>.</li> <li>Heinrich Beyer, Heinrich F. Beyer, H.-Jürgen Kluge, H.-J. Kluge, Viatcheslav Petrovich Shevelʹko, <i>X-Ray Radiation of Highly Charged Ions</i>, Springer Science & Business Media, 1997, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-63185-9" title="Special:BookSources/978-3-540-63185-9">978-3-540-63185-9</a>.</li> <li>Gillaspy, John, editor, <i>Trapping Highly Charged Ions: Fundamentals and Applications</i>, Edited by John Gillaspy. Published by <a href="/wiki/Nova_Science_Publishers,_Inc." class="mw-redirect" title="Nova Science Publishers, Inc.">Nova Science Publishers, Inc.</a>, Huntington, NY, 1999, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-56072-725-X" title="Special:BookSources/1-56072-725-X">1-56072-725-X</a>.</li> <li>Wolfgang Quint, Manuel Vogel, editors, <i>Fundamental Physics in Particle Traps</i>, Springer Tracts in Modern Physics, Volume 256 2014, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-45200-0" title="Special:BookSources/978-3-642-45200-0">978-3-642-45200-0</a>.</li></ul> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Forbidden_mechanism&oldid=1258023478">https://en.wikipedia.org/w/index.php?title=Forbidden_mechanism&oldid=1258023478</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Astronomical_spectroscopy" title="Category:Astronomical spectroscopy">Astronomical spectroscopy</a></li><li><a href="/wiki/Category:Quantum_chemistry" title="Category:Quantum chemistry">Quantum chemistry</a></li><li><a href="/wiki/Category:Spectroscopy" title="Category:Spectroscopy">Spectroscopy</a></li><li><a href="/wiki/Category:Nuclear_physics" title="Category:Nuclear physics">Nuclear physics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_uses_Ukrainian-language_script_(uk)" title="Category:CS1 uses Ukrainian-language script (uk)">CS1 uses Ukrainian-language script (uk)</a></li><li><a href="/wiki/Category:CS1_Ukrainian-language_sources_(uk)" title="Category:CS1 Ukrainian-language sources (uk)">CS1 Ukrainian-language sources (uk)</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_April_2015" title="Category:Articles with unsourced statements from April 2015">Articles with unsourced statements from April 2015</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_October_2023" title="Category:Articles needing additional references from October 2023">Articles needing additional references from October 2023</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 17 November 2024, at 19:22<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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