  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 rest-frame of the nucleus, around which an
electron, having linear velocity v and magnetic dipole-moment mu, travels in a
circular orbit. The interaction energy U is due to the coupling of the induced
electric dipole p=(v/c)x mu with the electric field En 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 Delta_E
= U/2, 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 factor for
the spin-orbit coupling energy is thus derived without the need to invoke the
well-known Thomas precession in the rest-frame of the electron.
