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Concept# Electron magnetic moment

Summary

In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment (symbol μe) is In units of the Bohr magneton (μB), it is -1.00115965218059μB, a value that was measured with a relative accuracy of 1.3e-13.
The electron is a charged particle with charge −e, where e is the unit of elementary charge. Its angular momentum comes from two types of rotation: spin and orbital motion. From classical electrodynamics, a rotating distribution of electric charge produces a magnetic dipole, so that it behaves like a tiny bar magnet. One consequence is that an external magnetic field exerts a torque on the electron magnetic moment that depends on the orientation of this dipole with respect to the field.
If the electron is visualized as a classical rigid body in which the mass and charge have identical distribution and motion that is rotating about an axis with angular momentum L, its magnetic dipole moment μ is given by:
where me is the electron rest mass. The angular momentum L in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. The ratio between the true spin magnetic moment and that predicted by this model is a dimensionless factor ge, known as the electron g-factor:
It is usual to express the magnetic moment in terms of the reduced Planck constant ħ and the Bohr magneton μB:
Since the magnetic moment is quantized in units of μB, correspondingly the angular momentum is quantized in units of ħ.
Classical notions such as the center of charge and mass are, however, hard to make precise for a quantum elementary particle. In practice the definition used by experimentalists comes from the form factors
appearing in the matrix element
of the electromagnetic current operator between two on-shell states. Here and are 4-spinor solution of the Dirac equation normalized so that , and is the momentum transfer from the current to the electron.

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