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I am currently learning for an exam and I wonder what the difference between the Lamb shift and the Darwin term is.

What I know is that the Darwin term affects only the s-states of the hydrogen atom and shifts its energy level to that of the p-state, while the Lamb shift affects the p-state and shifts its energy level, so that s- and p-states have different energies after all.

However, what I do not understand is that both are explained in terms of Zitterbewegung. The electron, as it moves around the nucleus, interacts with the electromagnetic field by emitting and absorbing virtual particles and experiences a recoil with each interaction. Thus, its distance from the nucleus varies by a certain $\delta r\approx \lambda_C$, which is accounted for in perturbation theory.

But, in this picture, what is here the actual cause for the Lamb shift and and what is the cause for the Darwin term?

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  • $\begingroup$ You do not cite this : Fine Structure Constant but from your question, you have possibly read it, or something pretty much like it, and it provides an answer, as far as I can see. $\endgroup$
    – user163104
    Jul 27, 2017 at 23:46
  • $\begingroup$ Yes, I read it and also the article about the Lamb shift but both are described in terms of zitterbewegung but there has to be a difference because the effect of Lamb shift and the Darwin term are different. $\endgroup$
    – Thomas Wening
    Jul 28, 2017 at 0:22
  • $\begingroup$ My best help to you here is to +1 nnd hope that you get a better answer than I can give you, I apologize, but my answer would not be good enough and might mislead you. $\endgroup$
    – user163104
    Jul 28, 2017 at 2:35

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Lamb shift is not due to the Zitterbewegung of the electron but to the fluctuation of the vacuum electric field which is not considered even in Dirac equation but in QED via electric field quantization. The electron in a hydrogen is affected by this fluctuation and feels additional Coulomb energy when very near the proton. The reason why the additional fine structure constant \alpha is included in the Lamb shift compared to the fine structure correction is that vacuum electric field exerts force to the electron: consider the equation of motion of electron in electric field. On the other hand Zitterbewegung can be described in Dirac equation and Darwin energy is naturally appear in the solution of Dirac equation and hence in the fine structure correction. In view of Dirac equation, Zitterbewegung occurs due to the interference between positive and negative energy electron states; in QED sense, Zitterbewegung results from electron-positron pair creations from vacuum. In short, Lamb shift appears as the result of electric field vacuum fluctuation while Darwin term due to the electron's trembled motion which originates from electron field vacuum fluctuation.

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