Lamb Shift - Experimental Work

Experimental Work

In 1947 Willis Lamb and Robert Retherford carried out an experiment using microwave techniques to stimulate radio-frequency transitions between and levels of hydrogen. By using lower frequencies than for optical transitions the Doppler broadening could be neglected (Doppler broadening is proportional to the frequency). The energy difference Lamb and Retherford found was a rise of about 1000 MHz of the level above the level.

This particular difference is a one-loop effect of quantum electrodynamics, and can be interpreted as the influence of virtual photons that have been emitted and re-absorbed by the atom. In quantum electrodynamics the electromagnetic field is quantized and, like the harmonic oscillator in quantum mechanics, its lowest state is not zero. Thus, there exist small zero-point oscillations that cause the electron to execute rapid oscillatory motions. The electron is "smeared out" and the radius is changed from to .

The Coulomb potential is therefore perturbed by a small amount and the degeneracy of the two energy levels is removed. The new potential can be approximated (using atomic units) as follows:

The Lamb shift itself is given by

with around 13 varying slightly with, and

with a small number (< 0.05).