Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei

TL;DR

This paper introduces a new Bogoliubov-based many-body perturbation theory for open-shell nuclei, offering a simple, accurate, and computationally efficient alternative to existing non-perturbative methods, demonstrated on various isotopic chains.

Contribution

It develops a novel Bogoliubov MBPT approach that simplifies calculations for open-shell nuclei while maintaining accuracy, extending the applicability of perturbation theory in nuclear physics.

Findings

Successfully applied to oxygen to nickel isotopic chains.

Achieved results comparable to non-perturbative methods.

Method's computational cost is independent of particle number.

Abstract

A novel Rayleigh-Schr\"odinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell fermionic systems. By choosing a reference state that solves the Hartree-Fock-Bogoliubov variational problem, the approach reduces to the well-tested M{\o}ller-Plesset, i.e., Hartree-Fock based, MBPT when applied to closed-shell systems. Due to its algorithmic simplicity, the newly developed framework provides a computationally simple yet accurate alternative to state-of-the-art non-perturbative many-body approaches. At the price of working in the quasi-particle basis associated with a single-particle basis of sufficient size, the computational scaling of the method is independent of the particle number. This paper presents the first realistic applications of the method ranging from the oxygen to the nickel isotopic chains on the basis of a modern nuclear Hamiltonian derived from chiral effective field theory.