5
$\begingroup$

Who first wrote down the spin-orbit coupling term in the atom? Was it Dirac himself? The term should be derived from the Dirac equation.

$\endgroup$

1 Answer 1

4
$\begingroup$

We can attribute the term to L. H. Thomas's The Kinematics of an Electron with an Axis (1927), derived a year before the Dirac equation was discovered. He writes

$\mathbf{K}=m[\mathbf{r}\times\mathbf{v}]$ is the angular momentum of revolution, and can be supposed nearly constant during one revolution, so the secular change in the direction of the spin axis is $$\frac{e}{mc}\mathbf{H}+\frac{1}{2}\frac{e^2}{mc^2}\frac{Z}{r^3}\mathbf{K}\tag{6.2}$$

This is for the case of, as Thomas puts it, a "Coulomb field"; $\mathbf{H}$ is an external magnetic field, and should not be confused with the Hamiltonian. The precession in this case is then $$\mathbf{\sigma}=\frac{1}{2}\frac{e^2}{mc^2}\frac{Z}{r^3}\mathbf{K}$$ The change in the Hamiltonian from the precession is then just $$\Delta H_T=\mathbf{\sigma}\cdot\mathbf{S}$$ although we could also apply this to $\text{(6.2)}$ in its entirety to get the full $\Delta H$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.