Title: Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Abstract

Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass A≈130 on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code ismore » implemented in m scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an N_max=6 spherical harmonic oscillator basis for ^16,18O and ¹⁸Ne in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while ²⁰O and ²⁰Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations. Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.« less

Authors:

Signoracci, Angelo J. ^[1]; Duguet, Thomas ^[2]; Hagen, Gaute ^[1]; Jansen, G. R. ^[3]

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+ Show Author Affiliations

1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2. Michigan State Univ., East Lansing, MI (United States)
3. Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:

Mon Jun 29 00:00:00 EDT 2015

Research Org.:

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1265773

Alternate Identifier(s):

OSTI ID: 1198603

Grant/Contract Number:  

AC05-00OR22725; DEFG02-96ER40963

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review C

Additional Journal Information:

Journal Volume: 91; Journal Issue: 6; Journal ID: ISSN 2469-9985

Publisher:

APS

Country of Publication:

United States

Language:

English

Subject:

73 NUCLEAR PHYSICS AND RADIATION PHYSICS