Precise Theory of the Zeeman Spectrum for Atomic Hydrogen and Deuterium and the Lamb Shift

In this paper we give a complete and straightforward analysis of the $n=2\mathrm{}$ Zeeman structure which is intrinsically accurate to 1 ppm for determining the Lamb shift from present experiments. This analysis takes into account the current experimental and theoretical knowledge of the atomic Hamiltonian. It is shown that the magnetic part of this Hamiltonian can be taken as that of a free electron and a free nucleus. Radiative corrections to this assumption are shown to be negligible. The total Hamiltonian can then be diagonalized in the $|F, j, l, m_F〉$ representation. Matrix representations of the Hamiltonian are given for all $n=2\mathrm{}$ states of hydrogen and deuterium. We give theoretical predictions for the $l=1\mathrm{}$ hyperfine intervals in hydrogen and deuterium which are accurate to 10 ppm. Values of the Lamb shift calculated from the recent Zeeman level crossings of Robiscoe and Cosens are tabulated.