4
$\begingroup$

I just want to confirm my understanding of spin-orbit coupling of a Hydrogen atom. Is the idea that the spin of the electron has a magnetic dipole moment and the orbit of the electron has a dipole moment as well. We know that dipole moments produce a magentic field, hence the dipole moment of the orbiting electron produces an magnetic field which exerts a torque on the dipole moment of the spin dipole magnetic moment.

Is this the basic idea? This seems strange, so the magnetic field of the electron (through the magnetic field of the orbit dipole moment) is exerting a force on itself (since the magnetic field of the orbit dipole moment exerts a force (torque) on the spin dipole moment)?

Would the picture then be as follows (where the orbital dipole moment is in the center and produces a magnetic field on the spin dipole vector located a distance $R$ away at the point of the electron). I understand that these are classical ideas for a quantum concept but I just want to get the best classical picture for now:

enter image description here

Thanks for any clarity.

Improve this question
$\endgroup$
2

3 Answers 3

Reset to default
2
$\begingroup$

The electron is moving at high speed through the radial electric field of the nucleaus. The Lorentz transformation of this electric field to the frame of the moving electron means that the electron sees a magnetic field in addition to the electric field. This magnetic field interacts with the electron's magnetic dipole momen to produce the spin-orbit coupling. There is also a purely kinematic effect "Thomas precession" that changes the coefficient.

The larger the charge on the nucleus, the faster the electron moves in its orbit and the bigger is the spin-orbit effect. This is why the effect is larger in heavy atoms further up the periodic table.

Improve this answer
$\endgroup$
0
$\begingroup$

Another way of understanding it, from a classical point of view is that, in the electron rest frame, the nucleus is orbiting the electron. Then you can imagine the electron feeling the magnetic field of the nucleus exerting a torque on its spin magnetic moment.

Improve this answer
New contributor
crdafisica is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
$\endgroup$
1
  • $\begingroup$ but that's not inertial frame $\endgroup$
    – Chandra Prakash
    Commented Dec 6 at 14:15
0
$\begingroup$

A moving magnetic dipole exhibits an electric dipole moment. This interacts with the nuclear field.

Improve this answer
$\endgroup$

Your Answer

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