Spin-Orbit interaction in nucleus' rest frame

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Discussion Overview

The discussion revolves around the spin-orbit interaction from the perspective of the nucleus's rest frame, exploring theoretical implications and mathematical formulations. Participants examine classical and quantum mechanical approaches to understand the interaction between the nucleus's magnetic field and the electron's spin magnetic moment, as well as the implications of relativistic effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that traditional discussions of spin-orbit interaction derive equations in the electron's rest frame and questions the necessity of a corresponding explanation from the nucleus's rest frame.
  • Another participant suggests that in the nucleus's rest frame, the interaction involves the electron's spin magnetic moment and the magnetic field produced by its orbital angular momentum, referencing the Liénard-Wiechert formula for retarded potentials.
  • A challenge is raised regarding the singularity of Liénard-Wiechert potentials at the source's location.
  • Further discussion indicates that the explanation in the electron's rest frame relies on the transformed electric field of the nucleus, proposing that a similar interaction in the nucleus's rest frame could involve the nucleus's electric field interacting with the electron's spin magnetic moment.
  • One participant proposes that a moving magnetic dipole acquires an electric dipole moment, which could interact with the nucleus's electric field.
  • Another participant introduces the Dirac Equation as a means to derive the Hamiltonian in any reference frame, discussing implications for the gyro factor and Thomas precession in the context of relativistic transformations.
  • Discussion includes the accuracy of measurements related to the electron's gyro factor and potential discrepancies in measurements for the muon, suggesting implications for physics beyond the standard model.
  • A question is posed about the nature of strong interaction contributions to radiative corrections, specifically regarding photon interactions with muons.
  • One participant describes the leading-order contribution involving QED triangle diagrams and self-energies, providing a reference for further reading.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate frameworks and implications of the spin-orbit interaction in different reference frames. There is no consensus on the best approach or the implications of the findings discussed.

Contextual Notes

Participants highlight limitations in existing models, including unresolved mathematical steps and the dependence on specific definitions related to the interactions discussed.

ShayanJ
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In all the places where Spin-Orbit interaction is discussed, the equations are derived by going to electron's rest frame and considering the interaction of nucleus' magnetic field with electrons spin magnetic moment. But from SR, we know that there as to be an explantion from the nucleus's rest frame too. But I have problem coming up with something!
Any ideas?
Thanks
 
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In the nucleus' rest frame, spin-orbit interaction is the electron's spin magnetic moment interacting with the magnetic field that the electron itself is producing due to its orbital angular momentum (hence the name). Classically, you'd need to use the Liénard-Wiechert formula for retarded potentials to compute the magnetic field at the electron's location at any time. I'm not entirely sure if that can be adapted quantum mechanically.
 
But Liénard-Wiechert potentials are singular at the source's location!
 
Hm, you're right...
 
Also the explanation in the electron's rest frame, is based on the magnetic field coming from transforming nucleus' electric field. So the explanation in the nucleus' rest frame should rely on some field produced by the nucleus.
The only thing that comes to my mind is a kind of interaction between nucleus' electric field with electron's spin magnetic moment but I don't remember any such interaction in EM!

I found it man!
A moving magnetic dipole acquires an electric dipole moment. And this electric dipole moment interacts with nucleus' electric field.
 
Using the Dirac Equation, which is relativistically covariant let's you write down the Hamiltonian directly in any reference frame you like. Case closed. The interesting point of the derivations in the non-relativistic realm is that you get, even for an elementary particle as the electron, where the Dirac Equation is applicable, you get gyro factor that is wrong by a factor of 2 when using the Galilei transformation at this point of the derivation. This is known as Thomas precession and marks the discovery of the Wigner rotation in the composition of two Lorentz boosts that are not in the same boost direction, which is completely missing in the Lorentz transformation.

Of course, the true gyro factor of the electron (and the other leptons) is not exactly 2 but (g-2) is one of the most accurately measured quantities which are (for the electron) in astonishing agreement with QED (at the four-loop order of perturbation theory!), while for the muon there may be a discrepancy with the standard model since the most accurate measurement of (g-2) performed at BNL shows a deviation by somewhat more than 3 standard deviations. This is not a discovery but only an evidence for physics beyond the standard model, and for this reason the entire experiment has been moved to Fermilab now and will be driven to even higher precision very soon. The main theoretical problem is the contribution from the strong interaction to the radiative corrections, which are somewhat larger for the muon than for the electron. These corrections have thus to be measured with high accuracy too. Such experiments at very low energies (in contrast to the largest energies in the experiments at LHC) are done in Mainz, and also their efforts towards even higher precision is under way. It's a very exciting issue in elementary-particle physics!
 
Last edited:
vanhees71 said:
contribution from the strong interaction to the radiative corrections
Is this referring to the process that the muon spontaneously radiates a photon, that photon decays to(I guess there is a better word for it!) a quark-antiquark pair and they annihilate each other to give a photon which is again absorbed by the muon?
 
The leading-order contribution is the QED triangle diagram with the exchanged photon dressed by self-energies involving hadrons and "light-by-light" scattering diagrams. For pictures of these diagrams and a review on the status, see

http://arxiv.org/abs/1311.2198
 

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