Origin of the spinorbit interaction
Abstract
We consider a semiclassical model to describe the origin of the spinorbit 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 {\boldsymbol{v}} and magnetic dipolemoment {\boldsymbol{μ }}, travels in a circular orbit. The interaction energy U is due to the coupling of the induced electric dipole {P}=({\boldsymbol{v}}/c)× {\boldsymbol{μ }} with the electric field {{\boldsymbol{E}}}_{n} of the nucleus. Assuming the radius of the electron’s orbit remains constant during a spinflip transition, our model predicts that the energy of the system changes by ∆ {E}=\frac{1}{2}U, the factor \frac{1}{2} emerging naturally as a consequence of equilibrium and the change of the kinetic energy of the electron. The correct \frac{1}{2} factor for the spinorbit coupling energy is thus derived without the need to invoke the wellknown Thomas precession in the restframe of the electron.
 Publication:

Physica Scripta
 Pub Date:
 August 2015
 DOI:
 10.1088/00318949/90/8/085501
 arXiv:
 arXiv:1506.07239
 Bibcode:
 2015PhyS...90h5501S
 Keywords:

 Physics  Atomic Physics
 EPrint:
 16 pages, 2 figures, 39 equations, 3 appendices, 33 references