Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Abstract

Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on the basis of realistic two- and three-nucleon interactions. Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of $U(1)$ gauge symmetry associated with particle number conservation, to account for their superfluid character. The present work formulates and applies Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wavefunction 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 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 eventually permit the treatment of doubly open-shell nuclei. Proof-of-principle calculations in an $N_{\text{max}}=6$ spherical harmonic oscillator basis are performed for ${}^{16,18,20}$O, ${}^{18}$Ne, ${}^{20}$Mg in the BCCD approximation with a chiral two-nucleon interaction, comparing to results obtained in standard coupled cluster theory when applicable. The breaking of $U(1)$ symmetry is monitored by computing the variance associated with the particle-number operator. 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 mid-mass 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.

22 pages, 13 figures

References in corpus (9)

• Chiral effective field theory and nuclear forces
• Three-body forces: From cold atoms to nuclei
• In-Medium Similarity Renormalization Group for Nuclei
• Coupled-cluster theory for three-body Hamiltonians
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
• Quasiparticle Coupled Cluster Theory for Pairing Interactions
• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• Ab initio coupled-cluster theory for open-shell nuclei
• Infrared extrapolations for atomic nuclei

Cited by in corpus (9)

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• Quasiparticle Coupled Cluster Theory for Pairing Interactions
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• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
• Gorkov algebraic diagrammatic construction formalism at third order
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• A Power Series Approximation in Symmetry Projected Coupled Cluster Theory
• Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions