Origin of the Spin-Orbit Interaction
Abstract
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.
Cite
@article{arxiv.1506.07239,
title = {Origin of the Spin-Orbit Interaction},
author = {Gianfranco Spavieri and Masud Mansuripur},
journal= {arXiv preprint arXiv:1506.07239},
year = {2015}
}
Comments
16 pages, 2 figures, 39 equations, 3 appendices, 33 references