Structure of Heavy Atoms: Three-Body Potentials

A discussion of the problem of the construction of a configuration-space Hamiltonian describing a many-electron atom with relativistic effects included is given. It appears that the total three-body energy in such an atom must be small if the problem of the construction of this Hamiltonian is to be simply solvable. To that end, a relativistic three-body potential is constructed for a three-electron system. It has novel terms which arise from a pathology of the two-body Hamiltonian previously noted. It is shown that a speculative generalization to the many-electron system results in a total three-body energy which may be many rydbergs but which is still a small perturbation on the total result.