Landé g-factor

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In physics, the Landé g-factor relates the magnetic dipole moment to the angular momentum of a quantum state. It is named after Alfred Landé, who first described it in 1921. The Landé g-factor is frequently referred to as the gyromagnetic ratio, especially when relating the dipole moment and angular momentum of an elementary particle.

In atomic physics, it 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 the degenerate states all sharing the same angular momentum. When the atom is placed in a weak magnetic field, the degeneracy is lifted.

The factor comes about during the calculation of the first-order perturbation in the energy of an atom when a weak uniform magnetic field (that is, weak in comparison to the system's internal magnetic field) is applied to the system. Formally we can write the factor as,

[g_J= g_L\frac+g_S\frac]

[ \approx 1+\frac]

[g_L\approx 1 , g_S\approx 2 ]

Here, J is the total electronic angular momentum, L is the orbital angular momentum, and S is the spin angular momentum. Because S=1/2 for electrons, one often sees this formula written with 3/4 in place of S(S+1).

If we wish to know the g-factor for an atom with total atomic angular momentum F=I+J,

[g_F= g_J\frac+g_I\frac]

[\approx g_J\frac ]

This last approximation is justified because [g_I] is smaller than [g_J] by the ratio of the electron mass to the proton mass.

Current Landé g-factor Values

Currently accepted NIST g-factor values[link]

Elementary Particle	g-factor	Uncertainty
Electron [g_]	-2.002 319 304 3718	0.000 000 000 0075
Neutron [g_]	-3.826 085 46	0.000 000 90
Proton [g_]	5.585 694 701	0.000 000 056
Muon [g_]	-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.

 

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