Ab initio Bogoliubov coupled cluster theory for openshell nuclei
Background: Ab initio manybody methods have been developed over the past 10 yr to address closedshell nuclei up to mass A≈130 on the basis of realistic two and threenucleon interactions. A current frontier relates to the extension of those manybody methods to the description of openshell nuclei. Several routes to address openshell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly openshell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particlenumber conservation as a way to account for their superfluid character. While this route was recently followed within the framework of selfconsistent 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 groundstate wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the groundstate energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes threenucleon forces at the normalordered twobody level. The first BCC code ismore »
 Authors:

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 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Michigan State Univ., East Lansing, MI (United States)
 Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725; DEFG0296ER40963
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 91; Journal Issue: 6; Journal ID: ISSN 24699985
 Publisher:
 APS
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
 OSTI Identifier:
 1265773
 Alternate Identifier(s):
 OSTI ID: 1198603
Signoracci, Angelo J., Duguet, Thomas, Hagen, Gaute, and Jansen, G. R.. Ab initio Bogoliubov coupled cluster theory for openshell nuclei. United States: N. p.,
Web. doi:10.1103/PhysRevC.91.064320.
Signoracci, Angelo J., Duguet, Thomas, Hagen, Gaute, & Jansen, G. R.. Ab initio Bogoliubov coupled cluster theory for openshell nuclei. United States. doi:10.1103/PhysRevC.91.064320.
Signoracci, Angelo J., Duguet, Thomas, Hagen, Gaute, and Jansen, G. R.. 2015.
"Ab initio Bogoliubov coupled cluster theory for openshell nuclei". United States.
doi:10.1103/PhysRevC.91.064320. https://www.osti.gov/servlets/purl/1265773.
@article{osti_1265773,
title = {Ab initio Bogoliubov coupled cluster theory for openshell nuclei},
author = {Signoracci, Angelo J. and Duguet, Thomas and Hagen, Gaute and Jansen, G. R.},
abstractNote = {Background: Ab initio manybody methods have been developed over the past 10 yr to address closedshell nuclei up to mass A≈130 on the basis of realistic two and threenucleon interactions. A current frontier relates to the extension of those manybody methods to the description of openshell nuclei. Several routes to address openshell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly openshell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particlenumber conservation as a way to account for their superfluid character. While this route was recently followed within the framework of selfconsistent 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 groundstate wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the groundstate energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes threenucleon forces at the normalordered twobody level. The first BCC code is implemented in m scheme, which will permit the treatment of doubly openshell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proofofprinciple calculations in an Nmax=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 twonucleon interaction, while 20O and 20Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particlenumber operator, is relatively constant for all five nuclei, in both the HartreeFockBogoliubov and BCCD approximations. Conclusions: The newly developed manybody formalism increases the potential span of ab initio calculations based on singlereference 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 openshell nuclei. Shortterm goals include the implementation of threenucleon forces at the normalordered twobody level. Midterm extensions include the approximate treatment of triples corrections and the development of the equationofmotion methodology to treat both excited states and odd nuclei. Longterm extensions include exact restoration of U(1) and SU(2) symmetries.},
doi = {10.1103/PhysRevC.91.064320},
journal = {Physical Review C},
number = 6,
volume = 91,
place = {United States},
year = {2015},
month = {6}
}