Converging many-body perturbation theory for ab-initio nuclear structure: Brillouin-Wigner perturbation series for closed-shell nuclei

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 derivations show that with optimal partitioning, 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 He4 and O16 with Daejeon16 and a bare N3LO potential in both harmonic-oscillator and Hartree-Fock bases confirm this finding.

Keywords

• Many-body perturbation theory
• Brillouin-Wigner
• Convergence criterion
• Ground-state energy