What is the difference between Lamb shift and the Darwin term?

Question

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?

Answer 1

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.