G-factor (physics)

A g-factor (also called g value) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is essentially a proportionality constant that relates the different observed magnetic moments μ of a particle to their angular momentum quantum numbers and a unit of magnetic moment (to make it dimensionless), usually the Bohr magneton or nuclear magneton. Its value is proportional to the gyromagnetic ratio. 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). 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 known of these is the electron spin g-factor (more often called simply the electron g-factor), ge, defined by where μs is the magnetic moment resulting from the spin of an electron, S is its spin angular momentum, and is the Bohr magneton. In atomic physics, the electron spin g-factor is often defined as the absolute value or negative of ge: The z-component of the magnetic moment then becomes The value gs is roughly equal to 2.002318, and is known to extraordinary precision - one part in 1013. The reason it is not precisely two is explained by quantum electrodynamics calculation of the anomalous magnetic dipole moment. The spin g-factor is related to spin frequency for a free electron in a magnetic field of a cyclotron: Secondly, the electron orbital g-factor, gL, is defined by where μL is the magnetic moment resulting from the orbital angular momentum of an electron, L is its orbital angular momentum, and μB is the Bohr magneton.