Converging Many-Body Perturbation Theory for Ab Initio Nuclear-Structure: I. Brillouin-Wigner Perturbation Series for Closed-Shell Nuclei

TL;DR

This paper develops a new approach to improve the convergence of many-body perturbation theory in nuclear physics, demonstrating that optimal partitionings ensure convergence regardless of interaction choice, supported by numerical results for helium-4 and oxygen-16.

Contribution

Introduces a Brillouin-Wigner perturbation series with a novel vertex function and a convergence criterion applicable to closed-shell nuclei, independent of interaction or basis.

Findings

Convergence criterion can always be satisfied with optimal partitionings.

Numerical results confirm convergence for 4He and 16O.

Method is basis- and interaction-independent.

Abstract

Convergence aspects of nuclear many-body perturbation theory for ground states of closed-shell nuclei are explored using a Brillouin-Wigner formulation with a new vertex function enabling high-order calculations. A general formalism for Hamiltonian partitioning and a convergence criterion for the perturbation series are proposed. Analytical derivation shows that with optimal partitionings, the convergence criterion for ground states can always be satisfied. This feature attributes to the variational principle and does not depend on the choice of an internucleon interaction or a many-body basis. Numerical calculations of the ground state energies of 4He and 16O with Daejeon16 and a bare N3LO potential in both harmonic-oscillator and Hartree-Fock bases confirm this finding.