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 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.
where μS is the total magnetic moment resulting from the spin of an electron, S is the magnitude of its spin angular momentum, and μB is the Bohr magneton. The z-component of the magnetic moment then becomes
The value gS is roughly equal to two, and is known to extraordinary accuracy. The reason it is not precisely two is explained by quantum electrodynamics.
where μL is the total magnetic moment resulting from the orbital angular momentum of an electron, L is the magnitude of its orbital angular momentum, and μB is the Bohr magneton. The value of gL is exactly equal to one, by a quantum-mechanical argument analogous to the derivation of the classical magnetogyric ratio. For an electron in an orbital with a magnetic quantum number ml, the z-component of the orbital angular momentum is
which, since gL = 1, is just μBml
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 μB is the Bohr magneton. The value of gJ is related to gL and gS by a quantum-mechanical argument; see the article Landé g-factor.
where μ is the magnetic moment resulting from the nuclear spin, I is the nuclear spin angular momentum, and μp is the nuclear magneton.
The muon, like the electron has a g-factor 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 mμ is the muon mass.
The muon g-factor can 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 uncertainy of 0.0000000013, compared to the theoretical prediction of 2.0023318361 with an uncertainty of 0.0000000010. This is a difference of 3.4 standard deviations, suggesting beyond-the-Standard-Model physics may be having an effect.
|Electron||2.002 319 304 3622||0.000 000 000 0015|
|Neutron||-3.826 085 46||0.000 000 90|
|Proton||5.585 694 701||0.000 000 056|
|Muon||2.002 331 8396||0.000 000 0012|
It should be noted that the electron g-factor is one of the most precisely measured values in physics, with its uncertainty beginning at the twelfth decimal place.