Origin of the spin-orbit interaction

We consider a semi-classical model to describe the origin of the spin-orbit interaction in a simple system such as the hydrogen atom. The interaction energy U is calculated in the restframe of the nucleus, around which an electron, having linear velocity ν and magnetic dipolemoment μ, travels in a circular orbit. The interaction energy U is due to the coupling of the induced electric dipole script P = (ν/c) x μ with the electric field E_n of the nucleus. Assuming the radius of the electron's orbit remains constant during a spin-flip transition, our model predicts that the energy of the system changes by Δ ε= 1/2U, the factor 1/2 emerging naturally as a consequence of equilibrium and the change of the kinetic energy of the electron. The correct 1/2 actor for the spin-orbit coupling energy is thus derived without the need to invoke the wellknown Thomas precession in the rest-frame of the electron.