A model-dependent approach to the non-relativistic Lamb shift

Abstract

The precise observation of the Lamb shift, between the $2s_{1/2}$ and $2p_{1/2}$ levels in hydrogen, was a genuine motivation for the development of modern quantum electrodynamics. According to Dirac theory, the $2s_{1/2}$ and $2p_{1/2}$ levels should have equal energies. However, “radiative corrections” due to the interaction between the atomic electron and the vacuum, shift the $2s_{1/2}$ level higher in energy by around $4.37493\times 10^{-6}$ eV or $ 2\pi\hbar\times 1057.85$ MHz relative to the $2p_{1/2}$ level. The measurement of Lamb and Retherford provided the stimulus for renormalization theory which has been so successful in handling troublesome divergences. The Lamb shift is still a central theme in atomic physics. W.E. Lamb was the first to see that this tiny shift, so elusive and hard to measure, would clarify in a fundamental way our thinking about particles and fields. In this article, the Lamb shift for the 2s energy level in hydrogen is assessed for three different electron models by using the variational principle. It is then verified that this shift arises mostly from the interaction of a bound electron with the zero-point fluctuations of the free electromagnetic field (Welton’s interpretation). We briefly comment on the construct validity of the proposed electron models.