Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Signoracci, Angelo J.; Duguet, Thomas; Hagen, Gaute; Jansen, G. R.

doi:10.1103/PhysRevC.91.064320

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

Journal Article · Mon Jun 29 00:00:00 EDT 2015 · Physical Review C

DOI:https://doi.org/10.1103/PhysRevC.91.064320· OSTI ID:1265773

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

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)

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 is 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.

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725; DEFG02-96ER40963

OSTI ID:: 1265773

Alternate ID(s):: OSTI ID: 1198603

Journal Information:: Physical Review C, Vol. 91, Issue 6; ISSN 2469-9985

Publisher:: APSCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 55 works

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