Hartree–Fock many-body perturbation theory for nuclear ground-states

Alexander Tichai,Sven Binder,Joachim Langhammer,Robert Roth

doi:10.1016/j.physletb.2016.03.029

Abstract

We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.

Highlights

The solution of the Schrödinger equation for atomic nuclei using realistic nuclear interactions is at the heart of ab initio nuclear structure theory
There exist a plethora of different ab initio methods, e.g., coupled cluster (CC) theory [1,2,3,4,5,6], in-medium similarity renormalization group (IM-SRG) [7,8,9,10,11], or self-consistent Green’s function methods [12,13,14]
A conceptually simple method to solve for the eigenenergies of a physical system is many-body perturbation theory (MBPT) [15,16,17]

Summary

Introduction

The solution of the Schrödinger equation for atomic nuclei using realistic nuclear interactions is at the heart of ab initio nuclear structure theory. Several studies of high-order MBPT based on Slater determinants constructed from harmonic oscillator (HO) single-particle states (HO-MBPT) have shown that the perturbation series is divergent in almost every case [18, 19]. In this Letter, we formulate MBPT based on Hartree-Fock (HF) single-particle states (HF-MBPT), and, for the first time, investigate the convergence behavior of the perturbation series up to 30th order.

Results

Conclusion