Radiative-recoil contributions to the Lamb shift

Abstract

We consider the proton mass corrections to the radiative Lamb shift in hydrogen. A procedure is developed to incorporate these contributions in the standard approach for obtaining the nonrecoil shifts. An equation given by Grotch and Yennie is used as a starting point to describe the hydrogen atom. This equation includes the Coulomb and the convection potentials as well as the proton kinetic energy. The radiative corrections then produce the desired radiative-recoil contributions. The complete lowest order (..cap alpha..(Z..cap alpha..)/sup 4/ m/sup 2//M) contributions as well as part of the higher order (..cap alpha..(Z..cap alpha..)/sup 5/ m/sup 2//M) contributions are derived analytically in the so-called external field approximation. In order to obtain residual ..cap alpha..(Z..cap alpha..)/sup 5/ m/sup 2//M contributions, we then consider perturbation kernels involving the two-photon exchange diagrams which are not already included in the external field approximation calculation. This is done utilizing the Fried--Yennie gauge for the radiative photon and the Coulomb gauge for the exchanged photons. The behavior of the perturbation kernels in the low-momentum region of the exchanged photon is analyzed in considerable detail. For the evaluation of the energy shift, the integrals are carried out numerically. The ..cap alpha..(Z..cap alpha..)/sup 5/ m/sup 2//M contributionmore » beyond the usual reduced mass correction is ..delta..E/sub n/ = (..cap alpha..(Z..cap alpha..)/sup 5//n/sup 3/) m/sup 2//M(-1.574+(-0.415 +- 0.004)) delta/sub l//sub 0/. For the 2S/sub 1/2/--2P/sub 1/2/ Lamb shift in hydrogen, this amounts to a contribution of (-2.527 +- 0.005) kHz.« less