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

TL;DR

This paper introduces a universal algorithm for calculating terms in atomic many-body perturbation theory, enabling flexible and efficient evaluation of complex diagrams across various many-body methods.

Contribution

It presents a novel, adaptable algorithm that simplifies and unifies the computation of perturbation theory terms and related many-body calculations.

Findings

Successfully calculated second and third order correlation corrections for sodium, copper, and gallium.

Determined hyperfine structure constants of sodium using the linearized single-double coupled cluster method.

Demonstrated the algorithm's versatility across different many-body theory applications.

Abstract

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.