Spherical coupled-cluster theory for open-shell nuclei

Abstract

A microscopic description of nuclei is important to understand the nuclear shell-model from fundamental principles. This is difficult to achieve for more than the lightest nuclei without an effective approximation scheme. The purpose of this paper is to define and evaluate an approximation scheme that can be used to study nuclei that are described as two particles attached to a closed (sub-)shell nucleus. The equation-of-motion coupled-cluster formalism has been used to obtain ground and excited state energies. This method is based on the diagonalization of a non-Hermitian matrix obtained from a similarity transformation of the many-body nuclear Hamiltonian. A chiral interaction at the next-to-next-to-next-to leading order using a cutoff at 500 MeV was used. The ground state energies of ${}^6$Li and ${}^6$He were in good agreement with a no-core shell-model calculation using the same interaction. Several excited states were also produced with overall good agreement. Only the $J^{\pi }=3^{+}$ excited state in ${}^6$Li showed a sizable deviation. The ground state energies of ${}^{18}$O, ${}^{18}$F and ${}^{18}$Ne were converged, but underbound compared to experiment. Moreover, the calculated spectra were converged and comparable to both experiment and shell-model studies in this region. Some excited states in ${}^{18}$O were high or missing in the spectrum. It was also shown that the wave function for both ground and excited states separates into an intrinsic part and a Gaussian for the center-of-mass coordinate. Spurious center-of-mass excitations are clearly identified.

23 pages, 17 figures. Accepted for publication in PRC

References in corpus (21)

• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Recent developments in no-core shell-model calculations
• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order
• Evolution of shell structure in neutron-rich calcium isotopes
• In-Medium Similarity Renormalization Group for Nuclei
• Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
• In-Medium Similarity Renormalization Group for Open-Shell Nuclei
• Ab-initio Gorkov-Green's function calculations of open-shell nuclei
• Medium-mass nuclei from chiral nucleon-nucleon interactions
• Corrections to nuclear energies and radii in finite oscillator spaces
• Universal properties of infrared oscillator basis extrapolations
• Solution of the center-of-mass problem in nuclear structure calculations
• Complex coupled-cluster approach to an ab-initio description of open quantum systems
• Benchmark calculations for 3H, 4He, 16O and 40Ca with ab-initio coupled-cluster theory
• Ab Initio Calculations of Medium-Mass Nuclei with Explicit Chiral 3N Interactions
• Ab initio computation of the 17F proton-halo state and resonances in A = 17 nuclei
• Ab-initio computation of neutron-rich oxygen isotopes
• Ab initio coupled-cluster theory for open-shell nuclei
• Spectroscopy of ${}^{26}$F to probe proton-neutron forces close to the drip line

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