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The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by [1] =, 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).
In atomic physics, the Landé g-factor is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field. The quantum states of electrons in atomic orbitals are normally degenerate in energy , with these degenerate states all sharing the same angular momentum.
Since a gyromagnetic factor equal to 2 follows from Dirac's equation, it is a frequent misconception to think that a g-factor 2 is a consequence of relativity; it is not. The factor 2 can be obtained from the linearization of both the Schrödinger equation and the relativistic Klein–Gordon equation (which leads to Dirac's).
Proposed Minimal Supersymmetric Standard Model one-loop corrections to the muon g−2 involving particles beyond the standard model: a neutralino and a smuon, and a chargino and a muon sneutrino respectively. The anomalous magnetic moment of the muon is calculated in a similar way to the electron.
is the gyromagnetic ratio for a particle of charge, [2] equal to , where is the mass of the precessing system, while is the g-factor of the system. The g-factor is the unit-less proportionality factor relating the system's angular momentum to the intrinsic magnetic moment; in classical physics it is 1 for any rigid object in which the charge ...
The most precise measurement comes from Brookhaven National Laboratory's muon g−2 experiment, [5] in which polarized muons are stored in a cyclotron and their spin orientation is measured by the direction of their decay electrons. As of February 2007, the current world average muon g-factor measurement is, [6] g/2 = 1.001 165 9208 (6),
The g-factor is a dimensionless factor associated to the nuclear magnetic moment. This parameter contains the sign of the nuclear magnetic moment, which is very important in nuclear structure since it provides information about which type of nucleon (proton or neutron) is dominating over the nuclear wave function.
where the quantity in square brackets is the Landé g-factor g J of the atom (= and ) and is the z-component of the total angular momentum. For a single electron above filled shells s = 1 / 2 {\displaystyle s=1/2} and j = l ± s {\displaystyle j=l\pm s} , the Landé g-factor can be simplified into: