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 allows the use of the same piece of computer code to evaluate any particular diagram in any specific order of the perturbation theory or to calculate similar terms in other areas of the many-body theory, like, e.g., terms in the coupled-cluster equations. The use of the algorithm is illustrated by calculating the second- and third-order correlation corrections to the removal energies of electrons from the ground state of sodium, copper and gallium and by calculating the hyperfine structure constants of sodium in the linearized single–double coupled cluster approximation.