G-factor (physics)

A g-factor (also called g value or dimensionless magnetic moment) is a dimensionless quantity that characterizes the magnetic moment and gyromagnetic ratio of an atom, a particle or nucleus. It is essentially a proportionality constant that relates the observed magnetic moment μ of a particle to its angular momentum quantum number and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton.

The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by

where μ is the spin magnetic moment of the particle, g is the g-factor of the particle, e is the elementary charge, m is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ħ/2 for Dirac particles).

Protons, neutrons, nuclei and other composite baryonic particles have magnetic moments arising from their spin (both of which may be zero). Conventionally, the associated g-factors are defined using the nuclear magneton, and thus implicitly using the proton's mass rather than the particle's mass as for a Dirac particle. The formula used under this convention is

where μ is the magnetic moment of the nucleon or nucleus resulting from its spin, g is the effective g-factor, I is its spin angular momentum, μ_N is the nuclear magneton, e is the elementary charge and m_p is the proton rest mass.

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 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 (more often called simply the electron g-factor), g_e, defined by

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