Relativistic and Radiative Interactions of Many-Electron Atoms in an External Magnetic Field

The effect of radiative corrections and of retardation in electron-electron interactions is discussed for a many-electron atom in an external homogeneous magnetic field. The results indicate that for $S$ states, corrections of relative order ${\alpha }^3{\mu }_{B}H$ are obtained by inclusion of Pauli interactions added to the Breit Hamiltonian of a many-electron atom coupled minimally to the external magnetic field. For states with nonzero orbital angular momentum additional order ${\alpha }^3{\mu }_{B}H$ corrections may be present. These arise from the Lamb-shift-type radiative correction combined with retardation corrections to the Breit potential.