I. Retardation Corrections in the Helium Atom. II. Self Energy of an Electron in a Magnetic Field

Part I. An analysis is made of the errors which arise for absolute levels and fine structure separations from the use, for the interaction of two electrons, of the nonretarded Breit expression instead of the true retarded interaction. The effects on the fine structure turn out to be too small for observation. The correction to the ground state energy may become observable if the experimental accuracy is increased. This is probably not the case for any excited level. Part II. The exact propagation function for a Dirac electron in an arbitrarily intense magnetic field is derived in closed form as a parametric integral. Using the exact relativistic wave functions and the exact of order e2, due to the emission and reabsorption in closed form as double parametric integrals. These integrals are shown to possess an asymptotic expansion in the small parameter H/m2. This expansion is not a pure power series but involves also terms of the form Hkln(m2/H). The terms of order H agrees with the known correction to the magnetic moment. The terms of order H2 and Hkln(m2/H) are exhibited and discussed.