Electron magnetic dipole moment

In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron caused by its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is approximately −9.284764×10−24 J/T. The electron magnetic moment has been measured to an accuracy of 7.6 parts in 1013. In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron caused by its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is approximately −9.284764×10−24 J/T. The electron magnetic moment has been measured to an accuracy of 7.6 parts in 1013. The electron is a charged particle with charge −1e, 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 electrically charged body creates a magnetic dipole with magnetic poles of equal magnitude but opposite polarity. This analogy does hold, since an electron indeed behaves like a tiny bar magnet. One consequence is that an external magnetic field exerts a torque on the electron magnetic moment depending on its orientation with respect to the field. If the electron is visualized as a classical charged particle literally rotating about an axis with angular momentum L, its magnetic dipole moment μ is given by where me is the electron rest mass. Note that the angular momentum L in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. It turns out that the classical result is off by a proportional factor for the spin magnetic moment. As a result, the classical result is corrected by multiplying it with a dimensionless correction factor g, known as the 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 F i ( q 2 ) {displaystyle F_{i}(q^{2})} appearing in the matrix element of the electromagnetic current operator between two on-shell states. Here u ( p i ) {displaystyle u(p_{i})} and u ¯ ( p f ) {displaystyle {ar {u}}(p_{f})} are 4-spinor solution of the Dirac equation normalized so that u ¯ u = 2 m e {displaystyle {ar {u}}u=2m_{ m {e}}} , and q μ = p f μ − p i μ {displaystyle q^{mu }=p_{f}^{mu }-p_{i}^{mu }} is the momentum transfer from the current to the electron. The q 2 = 0 {displaystyle q^{2}=0} form factor F 1 ( 0 ) = − e {displaystyle F_{1}(0)=-e} is the electron's charge, μ = ( F 1 ( 0 ) + F 2 ( 0 ) ) / 2 m e {displaystyle mu =(F_{1}(0)+F_{2}(0))/2m_{ m {e}}} is its static magnetic dipole moment, and − F 3 ( 0 ) / 2 m e {displaystyle -F_{3}(0)/2m_{ m {e}}} provides the formal definion of the electron's electric dipole moment. The remaining form factor F 4 ( q 2 ) {displaystyle F_{4}(q^{2})} would, if non zero, be the anapole moment. The spin magnetic moment is intrinsic for an electron. It is