无核壳模型的开壳核混合方法：能量计算的创新与效率提升

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本文主要探讨了无核壳模型（No-Core Shell Model, NCSM）与多构形扰动理论（Multi-Configurational Perturbation Theory, MCPT）的结合，提出了一种新型的混合多体计算方法。这种方法旨在解决开放壳核的基态和激发态能量问题，特别是在大型模型空间中，这通常对传统NCSM计算构成挑战。 NCSM以其灵活性著称，它在小模型空间中能够处理复杂的多粒子多配置态，但可能无法全面捕捉到大规模空间中的所有关联效应。为了解决这个问题，研究者利用了MCPT的高效性，通过二阶校正来弥补NCSM在处理复杂动态方面的不足。在这一过程中，首先在小模型空间中构建一个包含关键多粒子关联的多行列式参考状态，这是基础，然后通过MCPT对这个参考状态进行修正，以考虑到大模型空间中的额外关联。研究对象是偶数和奇数碳、氧和氟同位素，这些原子核由于具有开放的壳层结构，使得计算其能级变得尤为重要。作者将新方法与传统的大规模NCSM计算进行了对比，以验证其在精度和计算效率上的优势。这种方法的引入不仅提高了计算效率，还使得对复杂核体系的深入研究成为可能。本文的核心内容是开发了一种创新的核物理计算技术，它优化了无核壳模型和多构形扰动理论的协同作用，使得在处理开放壳核的能级问题时，能够在有限的计算资源下得到更精确的结果。这对于理解核力、核结构以及核反应等领域具有重要意义，也为未来更大规模的核物理计算提供了新的可能性。

Physics Letters B 786 (2018) 448–452

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Open-shell nuclei from No-Core Shell Model with perturbative

improvement

Alexander Tichai

a,b,∗

, Eskendr Gebrerufael

, Klaus Vobig

, Robert Roth

ESNT, CEA Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, France

Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstr. 2, 64289 Darmstadt, Germany

a r t i c l e i n f o a b s t r a c t

Article history:

Received

7 May 2018

Received

in revised form 11 October 2018

Accepted

16 October 2018

Available

online 19 October 2018

Editor:

J.-P. Blaizot

Keywords:

Perturbation

theory

initio

Many-body

theory

We introduce a hybrid many-body approach that combines the ﬂexibility of the No-Core Shell Model

(NCSM) with the eﬃciency of Multi-Conﬁgurational Perturbation Theory (MCPT) to compute ground-

and

excited-state energies in arbitrary open-shell nuclei in large model spaces. The NCSM in small

model spaces is used to deﬁne a multi-determinantal reference state that contains the most important

multi-particle multi-hole correlations and a subsequent second-order MCPT correction is used to capture

additional correlation effects from a large model space. We apply this new ab initio approach for the

calculation of ground-state and excitation energies of even and odd-mass carbon, oxygen, and ﬂuorine

isotopes and compare to large-scale NCSM calculations that are computationally much more expensive.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

The solution of the nuclear many-body problem with realis-

tic

interactions is at the heart of ab initio nuclear structure the-

ory.

In recent years tremendous progress has been made in the

ab initio description of nuclear observables, particularly in the

regime of medium-mass nuclei beyond the p-shell. Innovative ap-

proaches

like Coupled Cluster (CC) theory [1–6], In-Medium Sim-

ilarity

Renormalization Group (IM-SRG) [7–11], or Self-Consistent

Green’s function (SCGF) [12,13]have been established and provide

accurate descriptions of ground-states observables. In a previous

work we have shown that many-body perturbation theory (MBPT)

with Hartree–Fock single-particle orbitals yields rapidly convergent

perturbation series and that low-order partial sums are in agree-

ment

with state-of-the-art CC calculations [14], thus, adding to the

collection of eﬃcient medium-mass methods.

Despite

all the progress, the description of fully open-shell

medium-mass systems remains a challenge. The aforementioned

methods, in their basic formulation, are limited to ground states

of nuclei with closed sub-shells. The ground state of these nuclei

is dominated by a single Slater determinant that can serve as a

reference state for the construction of the fully correlated eigen-

Corresponding author.

E-mail

addresses: alexander.tichai@cea.fr (A. Tichai),

eskendr.gebrerufael@physik.tu-darmstadt.de (E. Gebrerufael),

klaus.vobig@physik.tu-darmstadt.de (K. Vobig), robert.roth@physik.tu-darmstadt.de

(R. Roth).

state. Several extensions have been developed to expand the range

of the single-determinant methods. Isotopes in the vicinity of shell

closures can be tackled by equation-of-motion techniques build on

the ground state of a neighbouring closed-shell nucleus [4]. Fur-

ther

away from shell closures, traditional shell-model approaches,

build on a closed-shell core and a small valence-space, combined

with non-perturbative valence-space interactions derived from ei-

ther

CC [15]or IM-SRG [16,17]have been used successfully.

important step towards a full no-core description of open-

shell

nuclei with multi-determinantal reference states is the

multi-reference formulation of the IM-SRG [11]. First applications

used particle-number projected Hartree–Fock–Bogoliubov refer-

ence

states for even-mass isotopes in semi-magic chains [18–20].

Moreover, we merged the multi-reference IM-SRG with the No-

Core

Shell Model (NCSM) [21–23]to address arbitrary even-mass

isotopes and excited states [24]. These methods are powerful and

eﬃcient but far from trivial, both, conceptually and algorithmi-

cally.

Recently, the concept of symmetry breaking has also been

applied in the framework of perturbation theory and ﬁrst ap-

plications

of particle-number-broken Bogoliubov MBPT have been

discussed [25].

this paper we present a much simpler approach, a combina-

tion

of the NCSM in small model spaces with a low-order MBPT

correction to capture correlations from a large space. This hybrid

method, for the ﬁrst time, allows to calculate nuclear ground-state

and excitation energies for all open-shell systems in large no-core

model spaces. After deﬁning the Hamiltonian, we review multi-

conﬁgurational

perturbation theory and discuss the combination

https://doi.org/10.1016/j.physletb.2018.10.029

0370-2693/

SCOAP

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