Production of Antihydrogen Beam and Development of Microwave Spectrometer to Measure the Lamb Shift

1.1 The Lamb Shift

In 1947, W. E. Lamb and R. C. Retherford carried out microwave (MW) spectroscopy on a hydrogen atom (H) where the magnetic field strength was varied, to find an energy split of around 1.05 GHz between the $2S_{1/2}$ and $2P_{1/2}$ levels.
While the Dirac equation explains the energy split between $2P_{1/2}$ and $2P_{3/2}$ levels of H atom caused by spin-orbit interaction, it cannot describe the removal of degeneracy between the $2_S{1/2}$ and $2P_{1/2}$ levels. Shortly after Lamb and Retherford’s experiment, H. A. Bethe’s theory, which considered the difference between the self-interaction of the electron in the hydrogen atom and that of a free electron, explained the mechanism of the Lamb shift.
This work paved a way to the renormalization theory, and quantum electrodynamics (QED), which integrated quantum mechanics and electromagnetism and was completed by S. Tomonaga, R. P. Feynman, J. Schwinger, and others. Today, the Lamb shift has been understood in the theory of quantum electrodynamics (QED), as an energy split contributed by such perturbative effects as electron’s self-energy, vacuum polarization, nuclear recoil effect, and so on.