Bogoliubov many-body perturbation theory for open-shell nuclei

A Tichai,P Arthuis,T Duguet,H Hergert,V Somà,R Roth

doi:10.1016/j.physletb.2018.09.044

Abstract

A Rayleigh–Schrödinger 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 Møller–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.

Highlights

Over the past two decades the ab initio description of nuclear structure properties has extended significantly both with respect to accessible mass numbers and to the open-shell character of the targeted system
In order to overcome this drawback, more general reference states are required, i.e., either multi-determinantal or symmetry-broken reference states. The latter were first used in nuclear structure through the Gorkov extension of self-consistent Green’s functions (SCGF) (GSCGF) that relies on a particle-number-broken Hartree–Fock–Bogoliubov (HFB) vacuum to describe singly-open-shell nuclei [17,18]
BMBPT calculations are benchmarked against well-established non-perturbative IT-no-core shell model (NCSM), GSCGF, and MR-in-medium similarity renormalization group (IMSRG) results for the same input Hamiltonian

Summary

Introduction

Over the past two decades the ab initio description of nuclear structure properties has extended significantly both with respect to accessible mass numbers and to the open-shell character of the targeted system. With the revival of perturbative techniques in nuclear structure theory [1,2] the concept of multideterminantal reference states inspired the development of a MBPT variant based on a NCSM reference state in a small model space, yielding the perturbatively-improved no-core shell model (NCSMPT). BMBPT calculations are benchmarked against well-established non-perturbative IT-NCSM, GSCGF, and MR-IMSRG results for the same input Hamiltonian

Many-body formalism

Hamiltonian

Low-order results in mid-mass nuclei

Conclusions