External Electromagnetic Interactions of Hydrogenic Atoms and Galilean Invariance
Abstract
The external electromagnetic interactions of hydrogenic atoms, which exhibit global Galilean invariance but preserve the relativistic description of the electron, are investigated. The Hamiltonian for the free atom consists of the Breit Hamiltonian for a relativistic electron interacting with a nonrelativistic spinless proton. Approximate generators of the Galilean group are constructed in terms of individualparticle position, momentum, and spin operators in several unitarily equivalent representations. In one of these the Hamiltonian is separable in conventional relative and centerofmass coordinates. This separability facilitates the treatment of a number of externalfield problems. An effective Hamiltonian for the interaction of the atom with a constant external electric field is given and compared to that obtained by other authors. The lowenergy theorem for Compton scattering from the composite system is explicitly verified including corrections due to atomic binding. This also gives an independent verification of recently obtained boundstate corrections to the atomic magnetic moment. Finally, an effective interaction of a charged Dirac particle with a hydrogenic atom is given in the representation in which the atomic Hamiltonian is separable.
 Publication:

Physical Review A
 Pub Date:
 February 1972
 DOI:
 10.1103/PhysRevA.5.527
 Bibcode:
 1972PhRvA...5..527G