Fundamentals of gauge-invariant relativistic many-body perturbation theory (PT) with optimized ab initio zeroth approximation in theory of relativistic multi-electron systems are presented. The problem of construction of optimal one-electron representation is directly linked with a problem of the correct accounting for multielectron exchange-correlation effects and gauge-invariance principle fulfilling in atomic calculations. New approach to construction of optimal PT zeroth approximation is based on accurate treating the lowest order multielectron effects, in particular, the gauge-dependent radiative contribution for the certain class of photon propagator (for instance, the Coulomb, Feynman, Babushkin ones) gauge. This value is considered to be a typical representative of important multielectron exchange-correlation effects, whose minimization is a reasonable criteria in the searching for optimal PT one-electron orbital basis. This procedure derives an undoubted profit in the routine many-body calculations as it provides the way of refinement of the atomic characteristics calculations, based on the “first principles”. The relativistic density-functional approximation is taken as the zeroth one. There have taken into account all exchange-correlation corrections of the second order and dominated classes of the higher orders diagrams (polarization interaction, quasiparticles screening, etc.). New form of multi-electron polarization functional is used. As illustration, the results of computing energies, transition probabilities for some heavy ions are presented.
Part of the book: Perturbation Theory