The electron magnetic moment and the gyromagnetic correction terms.

Golden Boar · science forum Guru Joined: 17 May 2005 Posts: 651

There is a constant called the mass-length constant as given below:

mC = m*lC = 3.51767e-43kg.m

where m is the mass, and lC is the Compton wavelength over 2 pi.

h = 2*pi*mC*c
hbar = mC*c
hdot = mC/2*c

where c is the speed of light in vacuum.

The spin angular momentum of an electron with spin s is given by:

ps = sqrt(s(s + 2)) * hdot

The allowed values for s are non-negative integers.

The corresponding magnetic moment in "classical" quantum mechanics is:

muB = Qp * lCe / 2 * c
muS = sqrt(s(s + 2)) * muB

where

Qp is the electric charge of the positron
lCe is the Compton wavelength over 2 pi of the electron
c is the speed of light
muS is the electron magnetic moment.

The ratio of the magnetic dipole moment to the mechanical angular
momentum, is then given by

gs = Qe / me

However, in quantum electrodynamics, the gyromagnetic ratio has
correction terms given in terms of the fine structure constant by

gs = [c1+c2+c3+c4...] * Qe / me

These correction terms lead to an elecron magnetic moment of

muE = [c1+c2+c3+c4...] * muB
muE = [c1+c2+c3+c4...] * Qp * lCe / 2 * c

where

c1 = 1+(alpha/(2*pi)
c2 = -0.328 * (alpha/pi)^2 = 2*pi*eta(0)*eta(1)+(197/144)-eta(2)-eta(3)
c3 = 1.181 * (alpha/pi)^3
c4 = -1.510 * (alpha/pi)^4

Google