Recoil contributions to the Lamb shift in the external-field approximation

The calculation of recoil corrections to the Lamb shift in hydrogen is carried out by treating the Dirac electron in the presence of the nuclear Coulomb and convection potentials. The leading Dirac equation and its solutions were given by Grotch and Yennie many years ago. A systematic derivation of recoil corrections to the leading Lamb shift leads to results in agreement with previous work. New terms of order α(Zα${)}^5$ $m^2$/M are derived by examining recoil corrections to higher-order radiative level shifts. These reduce the theoretical Lamb shift in the hydrogen n=2 state by about 2 ppm. It is expected, however, that additional contributions of the same order will also arise from corrections to the external-field approximation as well as from nonradiative recoil.