Gyromagnetic Ratio - Gyromagnetic Ratio For An Isolated Electron

Gyromagnetic Ratio For An Isolated Electron

An isolated electron has an angular momentum and a magnetic moment resulting from its spin. While an electron's spin is sometimes visualized as a literal rotation about an axis, it is in fact a fundamentally different, quantum-mechanical phenomenon with no true analogue in classical physics. Consequently, there is no reason to expect the above classical relation to hold. In fact it does not, giving the wrong result by a dimensionless factor called the electron g-factor, denoted g_e (or just g when there is no risk of confusion):

where μ_B is the Bohr magneton. As mentioned above, in classical physics one would expect the g-factor to be . However in the framework of relativistic quantum mechanics,

where is the fine-structure constant. Here the small corrections to the relativistic result come from the quantum field theory. Experimentally, the electron g-factor has been measured to twelve decimal places:

The electron gyromagnetic ratio is given by NIST as

The g-factor and γ are in excellent agreement with theory; see Precision tests of QED for details.