Spherical coupled-cluster theory for open-shell nuclei

Jansen, G. R.

doi:10.1103/physrevc.88.024305

Title: Spherical coupled-cluster theory for open-shell nuclei

Journal Article · Mon Aug 05 00:00:00 EDT 2013 · Physical Review C, Nuclear Physics

DOI:https://doi.org/10.1103/physrevc.88.024305· OSTI ID:1565057

Jansen, G. R. ^[1]

Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Oslo (Norway). Dept. of Physics and Center of Mathematics for Applications

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. 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 (N³LO) using a cutoff at 500 MeV was used. The ground-state energies of ⁶Li and ⁶He 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 $J^π = 3^+$ excited state in ⁶Li showed a sizable deviation. The ground-state energies of ¹⁸O, ¹⁸F, and ¹⁸Ne 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 ¹⁸O 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. Results are converged with respect to the size of the model space and the method can be used to describe nuclear states with simple structure. Especially the ground-state energies were very close to what has been achieved by exact diagonalization. To obtain a closer match with experimental data, effects of three-nucleon forces, the scattering continuum, as well as additional configurations in the coupled-cluster approximations are necessary.

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Research Organization:: Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725; FG02-96ER40963; SC0008499

OSTI ID:: 1565057

Journal Information:: Physical Review C, Nuclear Physics, Vol. 88, Issue 2; ISSN 0556-2813

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 29 works

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References (44)

Structure of $A = 10 - 13$ Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory Navrátil, P.; Gueorguiev, V. G.; Vary, J. P. Physical Review Letters, Vol. 99, Issue 4 https://doi.org/10.1103/PhysRevLett.99.042501	journal	July 2007
Ab initio Gorkov-Green's function calculations of open-shell nuclei Somà, V.; Barbieri, C.; Duguet, T. Physical Review C, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevC.87.011303	journal	January 2013
Ab Initio Study of ${}^{40}{Ca}$ with an Importance-Truncated No-Core Shell Model Roth, R.; Navrátil, P. Physical Review Letters, Vol. 99, Issue 9 https://doi.org/10.1103/PhysRevLett.99.092501	journal	August 2007
Benchmark calculations for ${}^{3}H$ , ${}^{4}{He}$ , ${}^{16}O$ , and ${}^{40}{Ca}$ with ab initio coupled-cluster theory Hagen, G.; Dean, D. J.; Hjorth-Jensen, M. Physical Review C, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevC.76.044305	journal	October 2007
Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT Musiał, Monika; Kucharski, Stanisław A.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 118, Issue 3 https://doi.org/10.1063/1.1527013	journal	January 2003
Improving upon CCSD(T): ΛCCSD(T). I. Potential energy surfaces Taube, Andrew G.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 128, Issue 4 https://doi.org/10.1063/1.2830236	journal	January 2008
In-medium similarity renormalization group with chiral two- plus three-nucleon interactions Hergert, H.; Bogner, S. K.; Binder, S. Physical Review C, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevC.87.034307	journal	March 2013
Toward open-shell nuclei with coupled-cluster theory Jansen, G. R.; Hjorth-Jensen, M.; Hagen, G. Physical Review C, Vol. 83, Issue 5 https://doi.org/10.1103/PhysRevC.83.054306	journal	May 2011
Similarity renormalization group for nucleon-nucleon interactions Bogner, S. K.; Furnstahl, R. J.; Perry, R. J. Physical Review C, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRevC.75.061001	journal	June 2007
Energy levels of light nuclei A = 18–19 Tilley, D. R.; Weller, H. R.; Cheves, C. M. Nuclear Physics A, Vol. 595, Issue 1 https://doi.org/10.1016/0375-9474(95)00338-1	journal	December 1995
Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order Ekström, A.; Baardsen, G.; Forssén, C. Physical Review Letters, Vol. 110, Issue 19 https://doi.org/10.1103/PhysRevLett.110.192502	journal	May 2013
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
Proton-neutron coupling in the Gamow shell model: The lithium chain Michel, N.; Nazarewicz, W.; Płoszajczak, M. Physical Review C, Vol. 70, Issue 6 https://doi.org/10.1103/PhysRevC.70.064313	journal	December 2004
Energy levels of light nuclei A=5, 6, 7 Tilley, D. R.; Cheves, C. M.; Godwin, J. L. Nuclear Physics A, Vol. 708, Issue 1-2 https://doi.org/10.1016/S0375-9474(02)00597-3	journal	September 2002
Convergent Theory for Effective Interaction in Nuclei Suzuki, K.; Lee, S. Y. Progress of Theoretical Physics, Vol. 64, Issue 6 https://doi.org/10.1143/PTP.64.2091	journal	December 1980
Solution of the Center-Of-Mass Problem in Nuclear Structure Calculations Hagen, G.; Papenbrock, T.; Dean, D. J. Physical Review Letters, Vol. 103, Issue 6 https://doi.org/10.1103/PhysRevLett.103.062503	journal	August 2009
Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions Hagen, G.; Papenbrock, T.; Dean, D. J. Physical Review C, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevC.82.034330	journal	September 2010
Universal properties of infrared oscillator basis extrapolations More, S. N.; Ekström, A.; Furnstahl, R. J. Physical Review C, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevC.87.044326	journal	April 2013
Ab initio computation of neutron-rich oxygen isotopes Hagen, G.; Papenbrock, T.; Dean, D. J. Physical Review C, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevC.80.021306	journal	August 2009
Ab initio calculations of medium-mass nuclei with explicit chiral 3 $N$ interactions Binder, Sven; Langhammer, Joachim; Calci, Angelo Physical Review C, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevC.87.021303	journal	February 2013
In-medium similarity renormalization group for open-shell nuclei Tsukiyama, K.; Bogner, S. K.; Schwenk, A. Physical Review C, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevC.85.061304	journal	June 2012
The weak coupling model applied to the nuclei with A = 16–19 Ellis, P. J.; Engeland, T. Nuclear Physics A, Vol. 144, Issue 1 https://doi.org/10.1016/0375-9474(70)90499-9	journal	March 1970
Chiral three-nucleon forces and bound excited states in neutron-rich oxygen isotopes Holt, J. D.; Menéndez, J.; Schwenk, A. The European Physical Journal A, Vol. 49, Issue 3 https://doi.org/10.1140/epja/i2013-13039-2	journal	March 2013
Modern ab initio approaches and applications in few-nucleon physics with Leidemann, Winfried; Orlandini, Giuseppina Progress in Particle and Nuclear Physics, Vol. 68 https://doi.org/10.1016/j.ppnp.2012.09.001	journal	January 2013
Discrete and Continuum Spectra in the Unified Shell Model Approach Volya, Alexander; Zelevinsky, Vladimir Physical Review Letters, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevLett.94.052501	journal	February 2005
New excited states in the halo nucleus 6He Mougeot, X.; Lapoux, V.; Mittig, W. Physics Letters B, Vol. 718, Issue 2 https://doi.org/10.1016/j.physletb.2012.10.054	journal	December 2012
The equation-of-motion coupled-cluster method. Applications to open- and closed-shell reference states Comeau, Donald C.; Bartlett, Rodney J. Chemical Physics Letters, Vol. 207, Issue 4-6 https://doi.org/10.1016/0009-2614(93)89023-B	journal	May 1993
Self-consistent Green's function method for nuclei and nuclear matter Dickhoff, W. H.; Barbieri, C. Progress in Particle and Nuclear Physics, Vol. 52, Issue 2 https://doi.org/10.1016/j.ppnp.2004.02.038	journal	April 2004
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties Stanton, John F.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 98, Issue 9 https://doi.org/10.1063/1.464746	journal	May 1993
Ab Initio Computation of the ${}^{17}F$ Proton Halo State and Resonances in $A = 17$ Nuclei Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M. Physical Review Letters, Vol. 104, Issue 18 https://doi.org/10.1103/PhysRevLett.104.182501	journal	May 2010
Recent developments in no-core shell-model calculations Navrátil, Petr; Quaglioni, Sofia; Stetcu, Ionel Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 8 https://doi.org/10.1088/0954-3899/36/8/083101	journal	May 2009
Corrections to nuclear energies and radii in finite oscillator spaces Furnstahl, R. J.; Hagen, G.; Papenbrock, T. Physical Review C, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevC.86.031301	journal	September 2012
Complex coupled-cluster approach to an ab-initio description of open quantum systems Hagen, G.; Dean, D. J.; Hjorth-Jensen, M. Physics Letters B, Vol. 656, Issue 4-5 https://doi.org/10.1016/j.physletb.2007.07.072	journal	November 2007
Continuum Effects and Three-Nucleon Forces in Neutron-Rich Oxygen Isotopes Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R. Physical Review Letters, Vol. 108, Issue 24 https://doi.org/10.1103/PhysRevLett.108.242501	journal	June 2012
Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory Entem, D. R.; Machleidt, R. Physical Review C, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevC.68.041001	journal	October 2003
Active-space equation-of-motion coupled-cluster methods for excited states of radicals and other open-shell systems: EA-EOMCCSDt and IP-EOMCCSDt Gour, Jeffrey R.; Piecuch, Piotr; Włoch, Marta The Journal of Chemical Physics, Vol. 123, Issue 13 https://doi.org/10.1063/1.2042452	journal	October 2005
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/RevModPhys.79.291	journal	February 2007
Spectroscopy of ${}^{26}F$ to Probe Proton-Neutron Forces Close to the Drip Line Lepailleur, A.; Sorlin, O.; Caceres, L. Physical Review Letters, Vol. 110, Issue 8 https://doi.org/10.1103/PhysRevLett.110.082502	journal	February 2013
Three-Body Forces and the Limit of Oxygen Isotopes Otsuka, Takaharu; Suzuki, Toshio; Holt, Jason D. Physical Review Letters, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevLett.105.032501	journal	July 2010
Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method Kucharski, Stanisław A.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 108, Issue 13 https://doi.org/10.1063/1.475961	journal	April 1998
Low momentum shell model effective interactions with all-order core polarizations Holt, Jason D.; Holt, Jeremy W.; Kuo, T. T. S. Physical Review C, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevC.72.041304	journal	October 2005
Evolution of Shell Structure in Neutron-Rich Calcium Isotopes Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.032502	journal	July 2012
Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT Musiał, Monika; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 119, Issue 4 https://doi.org/10.1063/1.1584657	journal	July 2003
Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: Application to Li6 and B10 Navrátil, P.; Caurier, E. Physical Review C, Vol. 69, Issue 1 https://doi.org/10.1103/PhysRevC.69.014311	journal	January 2004

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Coupled-cluster computations of atomic nuclei Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M. Reports on Progress in Physics, Vol. 77, Issue 9 https://doi.org/10.1088/0034-4885/77/9/096302	journal	September 2014
In-medium similarity renormalization group for closed and open-shell nuclei Hergert, H. Physica Scripta, Vol. 92, Issue 2 https://doi.org/10.1088/1402-4896/92/2/023002	journal	December 2016
Coupled-cluster computations of atomic nuclei Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M. arXiv https://doi.org/10.48550/arxiv.1312.7872	text	January 2013
Nonperturbative shell-model interactions from the in-medium similarity renormalization group Bogner, S. K.; Hergert, H.; Holt, J. D. arXiv https://doi.org/10.48550/arxiv.1402.1407	text	January 2014
Effects of three-nucleon forces and two-body currents on Gamow-Teller strengths Ekström, A.; Jansen, G. R.; Wendt, K. A. arXiv https://doi.org/10.48550/arxiv.1406.4696	text	January 2014
Emergent properties of nuclei from ab initio coupled-cluster calculations Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R. arXiv https://doi.org/10.48550/arxiv.1601.08203	text	January 2016
In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei Hergert, H. arXiv https://doi.org/10.48550/arxiv.1607.06882	text	January 2016
Ab Initio Excited States from the In-Medium Similarity Renormalization Group Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K. arXiv https://doi.org/10.48550/arxiv.1611.00661	text	January 2016
Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces Binder, S.; Calci, A.; Epelbaum, E. arXiv https://doi.org/10.48550/arxiv.1802.08584	text	January 2018

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