Force on an electric/magnetic dipole and classical approach to spin–orbit coupling in hydrogen-like atoms

We carry out the classical analysis of spin–orbit coupling in hydrogen-like atoms, using the modern expressions for the force and energy of an electric/magnetic dipole in an electromagnetic field. We disclose a novel physical meaning of this effect and show that for a laboratory observer the energy of spin–orbit interaction is represented solely by the mechanical energy of the spinning electron (considered as a gyroscope) due to the Thomas precession of its spin. Concurrently we disclose some errors in the old and new publications on this subject. - Highlights: • Classical analysis of spin–orbit coupling in a laboratory frame was erroneous. • Electromagnetic energy of electron in atom does not contribute to spin–orbit coupling. • Spin–orbit splitting results from the energy of Thomas precession of electron spin.