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| | Wilber Berryhill is what his spouse enjoys to contact him and he completely loves this name. Office supervising is exactly where her primary income comes from but she's currently applied for an additional one. The favorite hobby for him and his children is to perform lacross and he'll be starting some thing else along with it. Some time ago online psychic chat ([http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 cpacs.org]) she chose to live in Alaska and her parents live nearby.<br><br>Also visit my web-site: real [http://fashionlinked.com/index.php?do=/profile-13453/info/ email psychic readings] - [http://www.prograd.uff.br/novo/facts-about-growing-greater-organic-garden www.prograd.uff.br], |
| :''For the acceleration-related quantity in mechanics, see [[g-force|''g''-force]].''
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| A '''''g''-factor''' (also called '''''g'' value''' or '''dimensionless magnetic moment''') is a dimensionless quantity which characterizes the [[magnetic moment]] and [[gyromagnetic ratio]] of a particle or [[atomic nucleus|nucleus]]. It is essentially a proportionality constant that relates the observed magnetic moment μ of a particle to the appropriate [[angular momentum]] [[quantum number]] and the appropriate fundamental quantum unit of magnetism, usually the [[Bohr magneton]] or [[nuclear magneton]].
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| ==Calculation==
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| === Electron ''g''-factors ===
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| There are three magnetic moments associated with an electron: One from its [[Spin (physics)|spin angular momentum]], one from its [[azimuthal quantum number|orbital angular momentum]], and one from its total angular momentum (the quantum-mechanical sum of those two components). Corresponding to these three moments are three different ''g''-factors:
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| ==== Electron spin ''g''-factor ====
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| The most famous of these is the ''electron spin g-factor'' (more often called simply the ''electron g-factor''), ''g<sub>e</sub>'', defined by | |
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| :<math> \boldsymbol{\mu}_S = \frac{g_e\mu_\mathrm{B}}{\hbar}\boldsymbol{S}</math>
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| where '''''μ<sub>S</sub>''''' is the total magnetic moment resulting from the spin of an electron, '''''S''''' is its [[spin (physics)|spin]] angular momentum, and ''μ''<sub>B</sub> is the [[Bohr magneton]]. In atomic physics, the electron spin ''g''-factor is often defined as the ''absolute value'' or ''negative'' of ''g<sub>e</sub>'':
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| :<math>g_S = |g_e| = -g_e.</math>
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| The ''z''-component of the magnetic moment then becomes
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| :<math> \mu_z=-g_S \mu_\mathrm{B} m_s</math>
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| The value ''g<sub>S</sub>'' is roughly equal to 2.002319, and is known to extraordinary precision.<ref>{{cite journal|url=http://cerncourier.com/main/article/46/8/20 |title=Precision pins down the electron's magnetism|journal=CERN Courier|volume=46|issue=8|month=October|pages=35–37|first1=Gerald|last1= Gabrielse |first2= David|last2= Hanneke|year=2006}}</ref><ref>
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| {{cite journal
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| | title = New measurement of the electron magnetic moment using a one-electron quantum cyclotron
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| | year = 2006
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| | journal = [[Physical Review Letters]]
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| | volume = 97
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| | issue = 3
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| | pages = 030801
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| | doi = 10.1103/PhysRevLett.97.030801
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| | pmid=16907490
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| | bibcode=2006PhRvL..97c0801O
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| | last1 = Odom
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| | first1 = B.
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| | last2 = Hanneke
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| | first2 = D.
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| | last3 = d’Urso
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| | first3 = B.
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| | last4 = Gabrielse
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| | first4 = G.
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| }}</ref> The reason it is not ''precisely'' two is explained by [[quantum electrodynamics]] calculation of the [[anomalous magnetic dipole moment]].<ref>
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| {{cite journal
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| | title = A nonperturbative calculation of the electron's magnetic moment | |
| | year = 2004
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| | journal = [[Nuclear Physics B]]
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| | volume = 703
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| | issue = 1–2
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| | pages = 333–362
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| | doi = 10.1016/j.nuclphysb.2004.10.027
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| |arxiv = hep-ph/0406325 |bibcode = 2004NuPhB.703..333B
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| | last1 = Brodsky
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| | first1 = S
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| | last2 = Franke
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| | first2 = V
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| | last3 = Hiller
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| | first3 = J
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| | last4 = McCartor
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| | first4 = G
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| | last5 = Paston
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| | first5 = S
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| | last6 = Prokhvatilov
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| | first6 = E }}</ref>
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| ==== Electron orbital ''g''-factor ====
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| Secondly, the ''electron orbital g-factor'', ''g<sub>L</sub>'', is defined by
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| :<math> \boldsymbol{\mu}_L = -\frac{g_L \mu_\mathrm{B}}{\hbar}\boldsymbol{L}</math>
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| where '''''μ<sub>L</sub>''''' is the total magnetic moment resulting from the orbital angular momentum of an electron, '''''L''''' is the magnitude of its orbital angular momentum, and ''μ''<sub>B</sub> is the [[Bohr magneton]]. The value of ''g<sub>L</sub>'' is exactly equal to one, by a quantum-mechanical argument analogous to the derivation of the [[magnetogyric ratio|classical magnetogyric ratio]]. For an electron in an orbital with a [[magnetic quantum number]] m<sub>l</sub>, the ''z''-component of the orbital angular momentum is
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| :<math>\mu_z=g_L \mu_\mathrm{B} m_l</math>
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| which, since ''g<sub>L</sub>'' = 1, is just ''μ''<sub>B</sub>m<sub>l</sub>
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| ====Total angular momentum (Landé) ''g''-factor ====
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| Thirdly, the ''[[Landé g-factor]]'', ''g<sub>J</sub>'', is defined by
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| :<math> \boldsymbol{\mu} = -\frac{g_J \mu_\mathrm{B} }{\hbar}\boldsymbol{J}</math>
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| where '''''μ''''' is the total magnetic moment resulting from both spin and orbital angular momentum of an electron, '''''J''''' = '''''L'''''+'''''S''''' is its total angular momentum, and ''μ''<sub>B</sub> is the [[Bohr magneton]]. The value of ''g<sub>J</sub>'' is related to ''g<sub>L</sub>'' and ''g<sub>S</sub>'' by a quantum-mechanical argument; see the article [[Landé g-factor]].
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| === Nucleon and nucleus ''g''-factors ===
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| Protons, neutrons, and many nuclei have spin and magnetic moments, and therefore associated ''g''-factors. The formula conventionally used is
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| :<math> \boldsymbol{\mu} = \frac{g \mu_\mathrm{N}}{\hbar}\boldsymbol{I}</math>
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| where '''''μ''''' is the magnetic moment resulting from the nuclear spin, '''''I''''' is the nuclear spin angular momentum, ''μ''<sub>N</sub> is the [[nuclear magneton]], and ''g'' is the effective ''g''-factor.
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| === Muon ''g''-factor ===
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| [[Image:The muon g-2.svg|frame|If [[supersymmetry]] is realized in nature, there will be corrections to g-2 of the muon due to loop diagrams involving the new particles. Amongst the leading corrections are those depicted here: a [[neutralino]] and a [[smuon]] loop, and a [[chargino]] and a muon [[sneutrino]] loop. This represents an example of "beyond the Standard-Model" physics that might contribute to g-2.]]
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| The muon, like the electron has a ''g''-factor from its spin, given by the equation
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| :<math>\mathbf{\mu} = \frac{ge}{2m_\mu}\mathbf{S}</math>
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| where '''''μ''''' is the magnetic moment resulting from the muon’s spin, '''''S''''' is the spin angular momentum, and ''m<sub>μ</sub>'' is the muon mass.
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| The fact that the muon g-factor is not quite the same as the electron g-factor is mostly explained by quantum electrodynamics and its calculation of the [[anomalous magnetic dipole moment]]. Almost all of the small difference between the two values (99.96% of it) is due to a well-understood lack of a heavy-particle diagrams contributing to the probability for emission of a photon representing the magnetic dipole field, which are present for muons, but not electrons, in QED theory. These are entirely a result of the mass difference between the particles.
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| However, not all of the difference between the g-factors for electrons and muons are exactly explained by the quantum electrodynamics [[Standard Model]]. The muon ''g''-factor can, at least in theory, be affected by physics [[beyond the Standard Model]], so it has been measured very precisely, in particular at the [[Brookhaven National Laboratory]]. As of November 2006, the experimentally measured value is {{val|2.0023318416|(13)}}, compared to the theoretical prediction of {{val|2.0023318361|(10)}}.<ref>
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| {{cite journal
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| | last1 = Hagiwara
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| | first1 = K. |last2= Martin,|first2= A. D. |last3= Nomura|first3= Daisuke |last4= Teubner|first4= T.
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| | title = Improved predictions for g-2 of the muon and alpha(QED)(M(Z)**2)
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| | year = 2006
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| | doi = 10.1016/j.physletb.2007.04.012
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| | journal = Physics Letters B
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| | volume = 649
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| | issue = 2–3
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| | pages = 173–179
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| |arxiv = hep-ph/0611102 | bibcode=2007PhLB..649..173H
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| }}</ref> This is a difference of 3.4 [[standard deviation]]s, suggesting beyond-the-Standard-Model physics may be having an effect. The Brookhaven muon storage ring is being transported to Fermilab where the g-2 experiment will use it to make more precise measurements of muon g-factor.<ref>http://muon-g-2.fnal.gov/</ref>
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| == Measured ''g''-factor values ==
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| {| class="wikitable" style="text-align:center"
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| |-
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| ! Particle !! ''g''-factor !! Uncertainty
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| ! Electron <math>g_\mathrm{e}</math>
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| | {{gaps|−2.002|319|304|361|53}} || {{gaps|0.000|000|000|000|53}}
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| |-
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| ! Neutron <math>g_\mathrm{n}</math>
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| | {{gaps|−3.826|085|45}} || {{gaps|0.000|000|90}}
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| ! Proton <math>g_\mathrm{p}</math>
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| | {{gaps|5.585|694|713}} || {{gaps|0.000|000|046}}
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| |-
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| ! Muon <math>g_{\mu}</math>
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| | {{gaps|−2.002|331|8414}} || {{gaps|0.000|000|0012}}
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| |-
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| |+Currently accepted [[NIST]] ''g''-factor values <ref>{{cite web|work=NIST|title=CODATA values of the fundamental constants|url=http://physics.nist.gov/cgi-bin/cuu/Category?view=html&All+values.x=80&All+values.y=11}}</ref>
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| |}
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| The electron ''g''-factor is one of the most precisely measured values in physics, with a relative standard uncertainty of 2.6 x 10<sup>−13</sup>.
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| ==Notes and references==
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| {{reflist}}
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| ==See also==
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| *[[anomalous magnetic dipole moment]]
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| *[[Electron magnetic dipole moment]]
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| *[http://physics.nist.gov/cuu/Constants/codata.pdf CODATA recommendations 2006]
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| [[Category:Atomic physics]]
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| [[Category:Nuclear physics]]
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| [[Category:Particle physics]]
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| [[Category:Physical constants]]
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Wilber Berryhill is what his spouse enjoys to contact him and he completely loves this name. Office supervising is exactly where her primary income comes from but she's currently applied for an additional one. The favorite hobby for him and his children is to perform lacross and he'll be starting some thing else along with it. Some time ago online psychic chat (cpacs.org) she chose to live in Alaska and her parents live nearby.
Also visit my web-site: real email psychic readings - www.prograd.uff.br,