Coulomb-gauge electrodynamics analysis of two-photon exchange in electron-atom scattering

We analyze all the time-ordered two-photon-exchange Feynman diagrams for electron-atom scattering in the Coulomb gauge. This includes the exchange of Coulomb as well as transverse photons. At threshold energy, we recover the two-photon exchange potential previously obtained by Feinberg and Sucher using covariant field-dispersion-theory technique. The present calculation is an analog of the classical work of Casimir and Polder on the two-photon exchange between a pair of neutral atoms and bridges a gap between the covariant field-dispersion-theory calculation and other nonrelativistic calculations. The Casimir effect is manifested in the first nonadiabatic potential which changes from a $R^{\mathrm{-}6}$ dependence to a $R^{\mathrm{-}7}$ dependence at asymptotic distances (R>a/α). We calculate terms up to the order of (${\mathrm{hlambda}}_e$/R${)}^2$ or, equivalently, of order (a/R${)}^4$ compared to the classical electric dipole polarization potential, and include the lowest-order energy dependence beyond the threshold. The neglected terms are of order ${\alpha }^2$ or smaller at asymptotic distances. The present results are valid also for positron-atom scattering.