 gfactor (physics)

 For the accelerationrelated quantity in mechanics, see gforce.
A gfactor (also called g value or dimensionless magnetic moment) is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or 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.
Contents
Calculation
Electron gfactors
There are three magnetic moments associated with an electron: One from its spin angular momentum, one from its orbital angular momentum, and one from its total angular momentum (the quantummechanical sum of those two components). Corresponding to these three moments are three different gfactors:
Electron spin gfactor
The most famous of these is the electron spin gfactor (more often called simply the electron gfactor), g_{e}, defined by
where μ_{S} is the total magnetic moment resulting from the spin of an electron, S is the magnitude of its spin angular momentum, and μ_{B} is the Bohr magneton. In atomic physics, the electron spin gfactor is often defined as the absolute value or negative of g_{e}:
 g_{S} =  g_{e}  = − g_{e}.
The zcomponent of the magnetic moment then becomes
 μ_{z} = − g_{S}μ_{B}m_{s}
The value g_{S} is roughly equal to 2.002319, and is known to extraordinary accuracy.^{[1]}^{[2]} The reason it is not precisely two is explained by quantum electrodynamics calculation of the anomalous magnetic dipole moment.^{[3]}
Electron orbital gfactor
Secondly, the electron orbital gfactor, g_{L}, is defined by
where μ_{L} 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_{B} is the Bohr magneton. The value of g_{L} is exactly equal to one, by a quantummechanical argument analogous to the derivation of the classical magnetogyric ratio. For an electron in an orbital with a magnetic quantum number m_{l}, the zcomponent of the orbital angular momentum is
 μ_{z} = g_{L}μ_{B}m_{l}
which, since g_{L} = 1, is just μ_{B}m_{l}
Landé gfactor
Thirdly, the Landé gfactor, g_{J}, is defined by
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_{B} is the Bohr magneton. The value of g_{J} is related to g_{L} and g_{S} by a quantummechanical argument; see the article Landé gfactor.
Nucleon and nucleus gfactors
Protons, neutrons, and many nuclei have spin and magnetic moments, and therefore associated gfactors. The formula conventionally used is
where μ is the magnetic moment resulting from the nuclear spin, I is the nuclear spin angular momentum, μ_{N} is the nuclear magneton, and g is the effective gfactor.
Muon gfactor
The muon, like the electron has a gfactor from its spin, given by the equation
where μ is the magnetic moment resulting from the muon’s spin, S is the spin angular momentum, and m_{μ} is the muon mass.
The fact that the muon gfactor is not quite the same as the electron gfactor 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 wellunderstood lack of a heavyparticle 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.
However, not all of the difference between the gfactors for electrons and muons are exactly explained by the quantum electrodynamics Standard Model. The muon gfactor 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 2.0023318416 with an uncertainty of 0.0000000013, compared to the theoretical prediction of 2.0023318361 with an uncertainty of 0.0000000010.^{[4]} This is a difference of 3.4 standard deviations, suggesting beyondtheStandardModel physics may be having an effect.
Measured gfactor values
Elementary Particle gfactor Uncertainty Electron g_{e} −2.0023193043622 0.0000000000015 Neutron g_{n} −3.82608545 0.00000090 Proton g_{p} 5.585694713 0.000000046 Muon g_{μ} −2.0023318414 0.0000000012 Currently accepted NIST gfactor values ^{[5]} The electron gfactor is one of the most precisely measured values in physics, with its uncertainty beginning at the twelfth decimal place.
Notes and references
 ^ Gabrielse, Gerald; Hanneke, David (October 2006). "Precision pins down the electron's magnetism". CERN Courier 46 (8): 35–37. http://cerncourier.com/main/article/46/8/20.
 ^ Odom, B.; Hanneke, D.; d’Urso, B.; Gabrielse, G. (2006). "New measurement of the electron magnetic moment using a oneelectron quantum cyclotron". Physical Review Letters 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). "A nonperturbative calculation of the electron's magnetic moment". Nuclear Physics B 703 (1–2): 333–362. arXiv:hepph/0406325. Bibcode 2004NuPhB.703..333B. doi:10.1016/j.nuclphysb.2004.10.027.
 ^ Hagiwara, K.; Martin,, A. D.; Nomura, Daisuke; Teubner, T. (2006). "Improved predictions for g2 of the muon and alpha(QED)(M(Z)**2)". Physics Letters B 649 (2–3): 173–179. arXiv:hepph/0611102. doi:10.1016/j.physletb.2007.04.012.
 ^ "CODATA values of the fundamental constants". NIST. http://physics.nist.gov/cgibin/cuu/Category?view=html&All+values.x=80&All+values.y=11.
See also
Categories: Atomic physics
 Nuclear physics
 Particle physics
 Physical constants
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