skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantified Gamow shell model interaction for p s d -shell nuclei

Journal Article · · Physical Review C
 [1];  [2];  [1];  [3];  [4]
  1. Michigan State Univ., East Lansing, MI (United States). NSCL/FRIB Lab.
  2. Physics Inst. of Rosario (CONICET), Rosario (Argentina); National Univ. of Rosario (UNR), Rosario (Argentina). Faculty of Exact Sciences, Engineering and Surveying
  3. Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy, NSCL/FRIB Lab.
  4. Centre National de la Recherche Scientifique (CNRS), Caen (France). Centre de Recherche sur les Ions, les Matériaux et la Photonique (CIMAP), Grand Accelerateur National d'Ions Lourds (GANIL)

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the p-sd-shell interface. Method: The one-body potential of the 4He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon- 4He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A = 9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. In conclusion: The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the psd region of the nuclear chart.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Michigan State Univ., East Lansing, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
SC0013365; SC0008511; FG02-10ER41700
OSTI ID:
1435756
Alternate ID(s):
OSTI ID: 1409456
Journal Information:
Physical Review C, Vol. 96, Issue 5; ISSN 2469-9985
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 44 works
Citation information provided by
Web of Science

References (96)

Gamow shell model description of proton scattering on Ne 18 journal March 2014
Pairing correlations in nuclei on the neutron-drip line journal October 2005
Structure of unbound neutron-rich 9 He studied using single-neutron transfer journal September 2013
Effective Interactions in the Delta-Shells Potential journal February 2013
Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization journal November 2010
Editorial: Uncertainty Estimates journal April 2011
On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes journal February 1968
Intermediate Coupling in the 1 p -Shell journal January 1956
Invariant Forms of Interaction between Nuclear Particles journal June 1941
Chapter 1. Potential Model Approach journal January 1967
Resonant state expansion of the resolvent journal February 1993
Polarization measurements and phase shifts for p-4He scattering between 3 and 18 MeV journal March 1971
Challenges in nuclear structure theory journal March 2016
Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order journal May 2013
Energy levels of light nuclei A=5, 6, 7 journal September 2002
Momentum distribution and correlation of two-nucleon relative motion in He 6 and Li 6 journal August 2007
Pairing-induced localization of the particle continuum in weakly bound nuclei journal October 2000
On the normalization of Gamow functions journal January 1971
Description of the proton and neutron radiative capture reactions in the Gamow shell model journal March 2015
Cluster-orbital shell model and its application to the He isotopes journal July 1988
Chapter II. Theory of Resonating Group Method and Generator Coordinate Method, and Orthogonality Condition Model journal January 1977
Shell structure of exotic nuclei journal July 2007
Dynamics of quantum systems embedded in a continuum journal February 2003
Gamow shell model description of radiative capture reactions 6 Li( p , γ ) 7 Be and 6 Li( n , γ ) 7 Li journal March 2017
Shell Model Description of Weakly Bound Nuclei journal April 2005
Local chiral potentials with Δ -intermediate states and the structure of light nuclei journal November 2016
Coupled-cluster computations of atomic nuclei journal September 2014
Variational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei journal August 2008
Gamow shell model and realistic nucleon-nucleon interactions journal June 2006
Continuum effects in neutron-drip-line oxygen isotopes journal August 2017
Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects journal June 1996
The shell model as a unified view of nuclear structure journal June 2005
Fitting theories of nuclear binding energies journal May 2005
Statistical error analysis for phenomenological nucleon-nucleon potentials journal June 2014
Error estimates of theoretical models: a guide journal May 2014
Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances journal February 2015
Nuclear energy density optimization: Large deformations journal February 2012
Shell model in the complex energy plane journal October 2008
The Elastic Scattering of Protons by Alpha Particles journal January 1954
Two-Particle Resonant States in a Many-Body Mean Field journal July 2002
Alpha-deuteron model of the Li6 nucleus journal February 1961
Pair correlations near the neutron drip line journal August 1991
Gamow Shell Model Description of Neutron-Rich Nuclei journal July 2002
Error analysis of nuclear mass fits journal September 2008
Living on the edge of stability, the limits of the nuclear landscape journal January 2013
Forces in Molecules journal August 1939
Proton-neutron coupling in the Gamow shell model: The lithium chain journal December 2004
New analysis method of the halo phenomenon in finite many-fermion systems: First applications to medium-mass atomic nuclei journal May 2009
Chapter III. Study of Non-Alpha-Nuclei Based on the Viewpoint of Cluster Correlations journal January 1980
Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates journal October 2017
Nuclear energy density optimization journal August 2010
Lattice effective field theory for medium-mass nuclei journal May 2014
Ab initio no-core solutions for 6 Li journal May 2017
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei journal March 2016
Theoretical aspects of science with radioactive nuclear beams
  • Dobaczewski, Jacek; Nazarewicz, Witold
  • Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 356, Issue 1744 https://doi.org/10.1098/rsta.1998.0261
journal September 1998
Shell model in the complex energy plane and two-particle resonances journal January 2003
The Calculation of Errors by the Method of Least Squares journal April 1932
Determination of R-function and physical-state parameters for n-4He elastic scattering below 21 MeV journal September 1977
Density matrix renormalization group approach to two-fluid open many-fermion systems journal January 2009
Density Matrix Renormalization Group Approach for Many-Body Open Quantum Systems journal September 2006
Bootstrapping the statistical uncertainties of NN scattering data journal November 2014
Precise root-mean-square radius of He 4 journal April 2008
Alpha-deuteron structure of the 6Li ground state journal March 1969
Pairing and continuum effects in nuclei close to the drip line journal November 2001
Charge radii and neutron correlations in helium halo nuclei journal November 2011
Unified ab initio approaches to nuclear structure and reactions journal April 2016
Accurate nuclear radii and binding energies from a chiral interaction journal May 2015
Single-particle and collective motion in unbound deformed Mg 39 journal November 2016
Velocity dependence of the two-nucleon interaction journal June 1958
Studies in Intermediate Coupling: III The Lithium Isotopes journal March 1955
Phase shifts and polarization in proton-alpha scattering from 0.9 to 3.2 MeV journal January 1967
Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions journal February 2016
Spin-Orbit Coupling in the Proton-Proton Interaction journal July 1957
Quantum Monte Carlo methods for nuclear physics journal September 2015
Cluster-Model Study of the T=1 States in A=4 System: 3He+p Scattering journal October 1979
Gamow shell model description of weakly bound nuclei and unbound nuclear states journal May 2003
Error analysis of nuclear mass fits text January 2008
Density matrix renormalization group approach to two-fluid open many-fermion systems text January 2008
Isospin mixing and the continuum coupling in weakly bound nuclei text January 2009
Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization text January 2010
Effective interactions in the delta-shells potential text January 2012
Living on the edge of stability, the limits of the nuclear landscape text January 2012
Lattice Effective Field Theory for Medium-Mass Nuclei text January 2013
Coupled-cluster computations of atomic nuclei text January 2013
Error Estimates of Theoretical Models: a Guide text January 2014
Description of the proton and neutron radiative capture reactions in the Gamow shell model text January 2015
The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei text January 2015
Continuum effects in neutron-drip-line oxygen isotopes text January 2017
Gamow Shell Model Description of Neutron-Rich Nuclei text January 2002
Shell model in the complex energy plane and two-particle resonances text January 2002
Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States text January 2003
Proton-Neutron Coupling in the Gamow Shell Model: the Lithium Chain text January 2004
Fitting theories of nuclear binding energies text January 2004
Density matrix renormalization group approach for many-body open quantum systems text January 2006
Shell Structure of Exotic Nuclei text January 2007
Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects text January 1995

Cited By (4)