G-factor

From Wikipedia, the free encyclopedia

The correct title of this article is g-factor. The initial letter is shown capitalized due to technical restrictions.

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.

1 Electron g-factors
2 Nucleon and Nucleus g-factors
3 Muon g-factor
4 Measured g-factor Values
5 Notes and references
6 See also

[edit] Electron g-factors

There are three magnetic moments associated with an electron: The one from its spin angular momentum, the one from its orbital angular momentum, and the one from its total angular momentum (the quantum-mechanical sum of those two components). Corresponding to these three moments are three different g-factors.

The most famous of these is the electron spin g-factor, g_S (more often called simply the electron g-factor, g_e, when there is no risk of ambiguity), defined by

$\boldsymbol{\mu}_S=g_S \mu_\mathrm{B} (\boldsymbol{S}/\hbar)$

where μ_S is the magnetic moment resulting from the spin of an electron, S is its spin angular momentum, and μ_B is the Bohr magneton. The value g_S is roughly equal to negative two, but is known to extraordinary accuracy (Gabrielse, 2006).

Secondly, the electron orbital g-factor g_L is defined by

$\boldsymbol{\mu}_L=g_L \mu_\mathrm{B} (\boldsymbol{L}/\hbar)$

where μ_L is the magnetic moment resulting from the orbital angular momentum of an electron, L is its orbital angular momentum, and μ_B is the Bohr magneton. The value of g_L is exactly equal to one, by a quantum-mechanical argument analogous to the derivation of the classical magnetogyric ratio.

Thirdly, the Landé g-factor g_J is defined by

$\boldsymbol{\mu}=g_J \mu_\mathrm{B} (\boldsymbol{J}/\hbar)$

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 quantum-mechanical argument; see the article, Landé g-factor.

[edit] Nucleon and Nucleus g-factors

Protons, neutrons, and many nuclei have spin and magnetic moments, and are therefore associated with g-factors. The formula conventionally used is

$\boldsymbol{\mu}=g \mu_\mathrm{p} (\boldsymbol{I}/\hbar)$

where μ is the magnetic moment resulting from the nuclear spin, I is the nuclear spin angular momentum, and μ_p is the nuclear magneton.

[edit] Muon g-factor

The muon, like the electron has a g-factor from its spin, given by the equation

$\mathbf{\mu}=g (e\hbar/(2m_\mu)) (\mathbf{S}/\hbar)$

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.

One-loop MSSM corrections to the muon g-2 involving a neutralino and a smuon, and a chargino and a muon sneutrino respectively.

The muon g-factor can be affected by physics beyond the Standard Model, so 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^[1]. This is a difference of 3.4 standard deviations, suggesting beyond-the-Standard-Model physics may be having an effect.

[edit] Measured g-factor Values

Currently accepted NIST g-factor values[1]
Elementary Particle	g-factor	Uncertainty
Electron $g e$	-2.002 319 304 3718	0.000 000 000 0075
Neutron $g n$	-3.826 085 46	0.000 000 90
Proton $g p$	5.585 694 701	0.000 000 056
Muon $g μ$	-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 all of physics, with its uncertainty beginning at the twelfth decimal place.