g-factor (physics) - Wikipedia

A g-factor is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. g-factor(physics) FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch IthasbeensuggestedthatthisarticlebemergedwithGyromagneticratio.(Discuss)ProposedsinceAugust2022. Fortheacceleration-relatedquantityinmechanics,seeg-force. Ag-factor(alsocalledgvalueordimensionlessmagneticmoment)isadimensionlessquantitythatcharacterizesthemagneticmomentandangularmomentumofanatom,aparticleorthenucleus.Itisessentiallyaproportionalityconstantthatrelatesthedifferentobservedmagneticmomentsμofaparticletotheirangularmomentumquantumnumbersandaunitofmagneticmoment(tomakeitdimensionless),usuallytheBohrmagnetonornuclearmagneton. Contents 1Definition 1.1Diracparticle 1.2Baryonornucleus 2Calculation 2.1Electrong-factors 2.1.1Electronsping-factor 2.1.2Electronorbitalg-factor 2.1.3Totalangularmomentum(Landé)g-factor 2.2Muong-factor 3Measuredg-factorvalues 4Seealso 5Notesandreferences 6Furtherreading 7Externallinks Definition[edit] Diracparticle[edit] Thespinmagneticmomentofacharged,spin-1/2particlethatdoesnotpossessanyinternalstructure(aDiracparticle)isgivenby[1] μ = g e 2 m S , {\displaystyle{\boldsymbol{\mu}}=g{e\over2m}\mathbf{S},} whereμisthespinmagneticmomentoftheparticle,gistheg-factoroftheparticle,eistheelementarycharge,misthemassoftheparticle,andSisthespinangularmomentumoftheparticle(withmagnitudeħ/2forDiracparticles). Baryonornucleus[edit] Protons,neutrons,nucleiandothercompositebaryonicparticleshavemagneticmomentsarisingfromtheirspin(boththespinandmagneticmomentmaybezero,inwhichcasetheg-factorisundefined).Conventionally,theassociatedg-factorsaredefinedusingthenuclearmagneton,andthusimplicitlyusingtheproton'smassratherthantheparticle'smassasforaDiracparticle.Theformulausedunderthisconventionis μ = g μ N ℏ I = g e 2 m p I , {\displaystyle{\boldsymbol{\mu}}=g{\mu_{\text{N}}\over\hbar}{\mathbf{I}}=g{e\over2m_{\text{p}}}\mathbf{I},} whereμisthemagneticmomentofthenucleonornucleusresultingfromitsspin,gistheeffectiveg-factor,Iisitsspinangularmomentum,μNisthenuclearmagneton,eistheelementarychargeandmpistheprotonrestmass. Calculation[edit] Electrong-factors[edit] Therearethreemagneticmomentsassociatedwithanelectron:onefromitsspinangularmomentum,onefromitsorbitalangularmomentum,andonefromitstotalangularmomentum(thequantum-mechanicalsumofthosetwocomponents).Correspondingtothesethreemomentsarethreedifferentg-factors: Electronsping-factor[edit] Themostknownoftheseistheelectronsping-factor(moreoftencalledsimplytheelectrong-factor),ge,definedby μ s = g e μ B ℏ S {\displaystyle{\boldsymbol{\mu}}_{\text{s}}=g_{\text{e}}{\mu_{\text{B}}\over\hbar}\mathbf{S}} whereμsisthemagneticmomentresultingfromthespinofanelectron,Sisitsspinangularmomentum,and μ B = e ℏ / 2 m e {\displaystyle\mu_{\text{B}}=e\hbar/2m_{\text{e}}} istheBohrmagneton.Inatomicphysics,theelectronsping-factorisoftendefinedastheabsolutevalueornegativeofge: g s = | g e | = − g e . {\displaystyleg_{\text{s}}=|g_{\text{e}}|=-g_{\text{e}}.} Thez-componentofthemagneticmomentthenbecomes μ z = − g s μ B m s {\displaystyle\mu_{\text{z}}=-g_{\text{s}}\mu_{\text{B}}m_{\text{s}}} Thevaluegsisroughlyequalto2.002318,andisknowntoextraordinaryprecision.[2][3]Thereasonitisnotpreciselytwoisexplainedbyquantumelectrodynamicscalculationoftheanomalousmagneticdipolemoment.[4] Thesping-factorisrelatedtospinfrequencyforafreeelectroninamagneticfieldofacyclotron: ν s = g 2 ν c {\displaystyle\nu_{s}={\frac{g}{2}}\nu_{c}} Electronorbitalg-factor[edit] Secondly,theelectronorbitalg-factor,gL,isdefinedby μ L = − g L μ B ℏ L , {\displaystyle{\boldsymbol{\mu}}_{L}=-g_{L}{\mu_{\mathrm{B}}\over\hbar}\mathbf{L},} whereμListhemagneticmomentresultingfromtheorbitalangularmomentumofanelectron,Lisitsorbitalangularmomentum,andμBistheBohrmagneton.Foraninfinite-massnucleus,thevalueofgLisexactlyequaltoone,byaquantum-mechanicalargumentanalogoustothederivationoftheclassicalmagnetogyricratio.Foranelectroninanorbitalwithamagneticquantumnumberml,thez-componentoftheorbitalangularmomentumis μ z = − g L μ B m l {\displaystyle\mu_{\text{z}}=-g_{L}\mu_{\text{B}}m_{\text{l}}} which,sincegL=1,is−μBml Forafinite-massnucleus,thereisaneffectivegvalue[5] g L = 1 − 1 M {\displaystyleg_{L}=1-{\frac{1}{M}}} whereMistheratioofthenuclearmasstotheelectronmass. Totalangularmomentum(Landé)g-factor[edit] Thirdly,theLandég-factor,gJ,isdefinedby | μ J | = g J μ B ℏ | J | {\displaystyle|{\boldsymbol{\mu_{\text{J}}}}|=g_{J}{\mu_{\text{B}}\over\hbar}|\mathbf{J}|} whereμJisthetotalmagneticmomentresultingfrombothspinandorbitalangularmomentumofanelectron,J=L+Sisitstotalangularmomentum,andμBistheBohrmagneton.ThevalueofgJisrelatedtogLandgsbyaquantum-mechanicalargument;seethearticleLandég-factor.μJandJvectorsarenotcolinear,soonlytheirmagnitudescanbecompared. Muong-factor[edit] Ifsupersymmetryisrealizedinnature,therewillbecorrectionstog-2ofthemuonduetoloopdiagramsinvolvingthenewparticles.Amongsttheleadingcorrectionsarethosedepictedhere:aneutralinoandasmuonloop,andacharginoandamuonsneutrinoloop.Thisrepresentsanexampleof"beyondtheStandardModel"physicsthatmightcontributetog-2. Themuon,liketheelectron,hasag-factorassociatedwithitsspin,givenbytheequation μ = g e 2 m μ S , {\displaystyle{\boldsymbol{\mu}}=g{e\over2m_{\mu}}\mathbf{S},} whereμisthemagneticmomentresultingfromthemuon’sspin,Sisthespinangularmomentum,andmμisthemuonmass. Thatthemuong-factorisnotquitethesameastheelectrong-factorismostlyexplainedbyquantumelectrodynamicsanditscalculationoftheanomalousmagneticdipolemoment.Almostallofthesmalldifferencebetweenthetwovalues(99.96%ofit)isduetoawell-understoodlackofheavy-particlediagramscontributingtotheprobabilityforemissionofaphotonrepresentingthemagneticdipolefield,whicharepresentformuons,butnotelectrons,inQEDtheory.Theseareentirelyaresultofthemassdifferencebetweentheparticles. However,notallofthedifferencebetweentheg-factorsforelectronsandmuonsisexactlyexplainedbytheStandardModel.Themuong-factorcan,intheory,beaffectedbyphysicsbeyondtheStandardModel,soithasbeenmeasuredveryprecisely,inparticularattheBrookhavenNationalLaboratory.IntheE821collaborationfinalreportinNovember2006,theexperimentalmeasuredvalueis2.0023318416(13),comparedtothetheoreticalpredictionof2.00233183620(86).[6]Thisisadifferenceof3.4standarddeviations,suggestingthatbeyond-the-Standard-Modelphysicsmaybehavinganeffect.TheBrookhavenmuonstorageringwastransportedtoFermilabwheretheMuong-2experimentusedittomakemoreprecisemeasurementsofmuong-factor.OnApril7,2021,theFermilabMuong-2collaborationpresentedandpublishedanewmeasurementofthemuonmagneticanomaly.[7]WhentheBrookhavenandFermilabmeasurementsarecombined,thenewworldaveragediffersfromthetheorypredictionby4.2standarddeviations. Measuredg-factorvalues[edit] Particle Symbol g-factor Relativestandarduncertainty electron ge −2.00231930436256(35) 1.7×10−13[8] muon-(experiment-Brookhaven-2006) gμ −2.0023318418(13) 6.3×10−10[9] muon-(experiment-Fermilab-2021) gμ −2.0023318408(11) 5.4x10−10 muon-(experiment-world-average-2021) gμ −2.00233184121(82) 4.1x10−10 muon-(theory-June2020) gμ −2.00233183620(86) 4.3x10−10 neutron gn −3.82608545(90) 2.4×10−7[10] proton gp +5.5856946893(16) 2.9×10−10[11] NISTCODATArecommendedg-factorvalues[12] Theelectrong-factorisoneofthemostpreciselymeasuredvaluesinphysics. Seealso[edit] Anomalousmagneticdipolemoment Electronmagneticmoment Landég-factor Notesandreferences[edit] ^Povh,Bogdan;Rith,Klaus;Scholz,Christoph;Zetsche,Frank(2013-04-17).ParticlesandNuclei.ISBN 978-3-662-05023-1. ^Gabrielse,Gerald;Hanneke,David(October2006)."Precisionpinsdowntheelectron'smagnetism".CERNCourier.46(8):35–37.Archivedfromtheoriginalon2006-10-18.Retrieved2007-05-27. ^Odom,B.;Hanneke,D.;d’Urso,B.;Gabrielse,G.(2006)."Newmeasurementoftheelectronmagneticmomentusingaone-electronquantumcyclotron".PhysicalReviewLetters.97(3):030801.Bibcode:2006PhRvL..97c0801O.doi:10.1103/PhysRevLett.97.030801.PMID 16907490. ^Brodsky,S;Franke,V;Hiller,J;McCartor,G;Paston,S;Prokhvatilov,E(2004)."Anonperturbativecalculationoftheelectron'smagneticmoment".NuclearPhysicsB.703(1–2):333–362.arXiv:hep-ph/0406325.Bibcode:2004NuPhB.703..333B.doi:10.1016/j.nuclphysb.2004.10.027.S2CID 118978489. ^Lamb,WillisE.(1952-01-15)."FineStructureoftheHydrogenAtom.III".PhysicalReview.85(2):259–276.Bibcode:1952PhRv...85..259L.doi:10.1103/PhysRev.85.259.PMID 17775407. ^Hagiwara,K.;Martin,A.D.;Nomura,Daisuke;Teubner,T.(2007)."Improvedpredictionsforg-2ofthemuonandαQED(M2Z)".PhysicsLettersB.649(2–3):173–179.arXiv:hep-ph/0611102.Bibcode:2007PhLB..649..173H.doi:10.1016/j.physletb.2007.04.012.S2CID 118565052. ^B.Abi;et al.(Muong-2collaboration)(7April2021)."MeasurementofthePositiveMuonAnomalousMagneticMomentto0.46ppm".PhysicalReviewLetters.126(14):141801.arXiv:2104.03281.doi:10.1103/PhysRevLett.126.141801.ISSN 0031-9007. ^"2018CODATAValue:electrongfactor".TheNISTReferenceonConstants,Units,andUncertainty.NIST.20May2019.Retrieved2020-03-13. ^"2018CODATAValue:muongfactor".TheNISTReferenceonConstants,Units,andUncertainty.NIST.20May2019.Retrieved2019-05-20. ^"CODATAValue:Neutrongfactor".NIST.Retrieved5November2017. ^"2018CODATAValue:protongfactor".TheNISTReferenceonConstants,Units,andUncertainty.NIST.June2015.Retrieved2019-03-08. ^"CODATAvaluesofthefundamentalconstants".NIST. Furtherreading[edit] CODATArecommendations2006 Externallinks[edit] MediarelatedtoG-factor(physics)atWikimediaCommons Gwinner,Gerald;Silwal,Roshani(June2022)."Tinyisotopicdifferencetestsstandardmodelofparticlephysics".Nature.606(7914):467–468.doi:10.1038/d41586-022-01569-3. 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