Relativistic and Non-Relativistic Many-Body Procedure, Applied to Atomic Systems

A review is given of the non-relativistic many-body perturbation theory (MBPT), emphasizing the diagrammatic expansion and the all-order procedures, such as the coupled-cluster approach. Illustrative numerical examples are given. More recent formal developments, concerning incomplete model space and hermitian effective hamiltonian, are also mentioned. Various approximate schemes currently in use for relativistic many-body calculations are discussed and analysed from the point of QED. The “no-virtual-pair approximation”, which contains the all-order non-relativistic MBPT as well as the leading relativistic corrections, is applied to He-like systems. Possibilities are discussed of going beyond that scheme for general many-electron systems in a rigorous and systematic way.