An universal algorithm of calculating terms of atomic many-body perturbation theory

An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm assumes a basis set of orthogonal single-electron orbitals supplied by the user. These orbitals are the eigenstates of the Dirac operator in the spherically-symmetric case. Apart from this the algorithm is practically free from any limitations and can be used for calculating of wide range of atomic properties in any order of the perturbation theory and with any external field applied to the atom. The use of the algorithm is illustrated by calculating of the second and third order correlation corrections to the ground state energies of sodium, copper and gallium.