Quantified Gamow shell model interaction for $psd$ shell nuclei
Abstract
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 complexenergy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant manybody 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 (onebody and twobody) interaction in the psdfshellmodel space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the psdshell interface. Method: The onebody potential of the ^{4}He core is modeled by a WoodsSaxon + spinorbit + Coulomb potential, and the finiterange nucleonnucleon interaction between the valence nucleons consists of central, spinorbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ ^{2} optimization is performed using the GaussNewton algorithm augmented by the singular value decomposition technique. The resulting covariancemore »
 Authors:

 Michigan State Univ., East Lansing, MI (United States). NSCL/FRIB Lab.
 Physics Inst. of Rosario (CONICET), Rosario (Argentina); National Univ. of Rosario (UNR), Rosario (Argentina). Faculty of Exact Sciences, Engineering and Surveying
 Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy, NSCL/FRIB Lab.
 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)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Michigan State Univ., East Lansing, MI (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1435756
 Alternate Identifier(s):
 OSTI ID: 1409456
 Grant/Contract Number:
 SC0013365; SC0008511; FG0210ER41700
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Jaganathen, Y., Betan, R. M. Id, Michel, N., Nazarewicz, W., and P?oszajczak, M. Quantified Gamow shell model interaction for psd shell nuclei. United States: N. p., 2017.
Web. doi:10.1103/PhysRevC.96.054316.
Jaganathen, Y., Betan, R. M. Id, Michel, N., Nazarewicz, W., & P?oszajczak, M. Quantified Gamow shell model interaction for psd shell nuclei. United States. doi:10.1103/PhysRevC.96.054316.
Jaganathen, Y., Betan, R. M. Id, Michel, N., Nazarewicz, W., and P?oszajczak, M. Mon .
"Quantified Gamow shell model interaction for psd shell nuclei". United States. doi:10.1103/PhysRevC.96.054316. https://www.osti.gov/servlets/purl/1435756.
@article{osti_1435756,
title = {Quantified Gamow shell model interaction for psd shell nuclei},
author = {Jaganathen, Y. and Betan, R. M. Id and Michel, N. and Nazarewicz, W. and P?oszajczak, M.},
abstractNote = {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 complexenergy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant manybody 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 (onebody and twobody) interaction in the psdfshellmodel space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the psdshell interface. Method: The onebody potential of the 4He core is modeled by a WoodsSaxon + spinorbit + Coulomb potential, and the finiterange nucleonnucleon interaction between the valence nucleons consists of central, spinorbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ2 optimization is performed using the GaussNewton 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 onebody potential reproduces nucleon 4He scattering phase shifts up to an excitation energy of 20 MeV. The twobody interaction built on top of the optimized onebody field is adjusted to the bound and unbound groundstate 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 twonucleon 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.},
doi = {10.1103/PhysRevC.96.054316},
journal = {Physical Review C},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {11}
}
Web of Science
Works referenced in this record:
Gamow shell model description of proton scattering on ${}^{18}\mathrm{Ne}$
journal, March 2014
 Jaganathen, Y.; Michel, N.; Płoszajczak, M.
 Physical Review C, Vol. 89, Issue 3
Pairing correlations in nuclei on the neutrondrip line
journal, October 2005
 Hagino, K.; Sagawa, H.
 Physical Review C, Vol. 72, Issue 4
Structure of unbound neutronrich ${}^{9}$ He studied using singleneutron transfer
journal, September 2013
 Al Kalanee, T.; Gibelin, J.; RousselChomaz, P.
 Physical Review C, Vol. 88, Issue 3
Effective Interactions in the DeltaShells Potential
journal, February 2013
 Navarro Pérez, R.; Amaro, J. E.; Ruiz Arriola, E.
 FewBody Systems, Vol. 54, Issue 710
Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and preoptimization
journal, November 2010
 Stoitsov, M.; Kortelainen, M.; Bogner, S. K.
 Physical Review C, Vol. 82, Issue 5
Editorial: Uncertainty Estimates
journal, April 2011
 The Editors,
 Physical Review A, Vol. 83, Issue 4
On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes
journal, February 1968
 Berggren, Tore
 Nuclear Physics A, Vol. 109, Issue 2
Intermediate Coupling in the $1p$ Shell
journal, January 1956
 Kurath, Dieter
 Physical Review, Vol. 101, Issue 1
Invariant Forms of Interaction between Nuclear Particles
journal, June 1941
 Eisenbud, L.; Wigner, E. P.
 Proceedings of the National Academy of Sciences, Vol. 27, Issue 6
Chapter 1. Potential Model Approach
journal, January 1967
 Tamagaki, Ryozo; Watari, Wataro
 Progress of Theoretical Physics Supplement, Vol. 39
Resonant state expansion of the resolvent
journal, February 1993
 Berggren, Tore; Lind, Patric
 Physical Review C, Vol. 47, Issue 2
Polarization measurements and phase shifts for p4He scattering between 3 and 18 MeV
journal, March 1971
 Schwandt, P.; Clegg, T. B.; Haeberli, W.
 Nuclear Physics A, Vol. 163, Issue 2
Challenges in nuclear structure theory
journal, March 2016
 Nazarewicz, W.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 43, Issue 4
Optimized Chiral NucleonNucleon Interaction at NexttoNexttoLeading Order
journal, May 2013
 Ekström, A.; Baardsen, G.; Forssén, C.
 Physical Review Letters, Vol. 110, Issue 19
Energy levels of light nuclei A=5, 6, 7
journal, September 2002
 Tilley, D. R.; Cheves, C. M.; Godwin, J. L.
 Nuclear Physics A, Vol. 708, Issue 12
Momentum distribution and correlation of twonucleon relative motion in ${}^{6}\mathrm{He}$ and ${}^{6}\mathrm{Li}$
journal, August 2007
 Horiuchi, W.; Suzuki, Y.
 Physical Review C, Vol. 76, Issue 2
Pairinginduced localization of the particle continuum in weakly bound nuclei
journal, October 2000
 Fayans, S. A.; Tolokonnikov, S. V.; Zawischa, D.
 Physics Letters B, Vol. 491, Issue 34
On the normalization of Gamow functions
journal, January 1971
 Gyarmati, B.; Vertse, T.
 Nuclear Physics A, Vol. 160, Issue 3
Description of the proton and neutron radiative capture reactions in the Gamow shell model
journal, March 2015
 Fossez, K.; Michel, N.; Płoszajczak, M.
 Physical Review C, Vol. 91, Issue 3
Clusterorbital shell model and its application to the He isotopes
journal, July 1988
 Suzuki, Y.; Ikeda, K.
 Physical Review C, Vol. 38, Issue 1
Chapter II. Theory of Resonating Group Method and Generator Coordinate Method, and Orthogonality Condition Model
journal, January 1977
 Saito, Sakae
 Progress of Theoretical Physics Supplement, Vol. 62
Shell structure of exotic nuclei
journal, July 2007
 Dobaczewski, J.; Michel, N.; Nazarewicz, W.
 Progress in Particle and Nuclear Physics, Vol. 59, Issue 1
Dynamics of quantum systems embedded in a continuum
journal, February 2003
 Okołowicz, J.; Płoszajczak, M.; Rotter, I.
 Physics Reports, Vol. 374, Issue 45
Isospin mixing and the continuum coupling in weakly bound nuclei
journal, October 2010
 Michel, N.; Nazarewicz, W.; Płoszajczak, M.
 Physical Review C, Vol. 82, Issue 4
Dependence of singleparticle energies on coupling constants of the nuclear energy density functional
journal, June 2008
 Kortelainen, M.; Dobaczewski, J.; Mizuyama, K.
 Physical Review C, Vol. 77, Issue 6
Gamow shell model description of radiative capture reactions ^{6} Li( p , γ ) ^{7} Be and ^{6} Li( n , γ ) ^{7} Li
journal, March 2017
 Dong, G. X.; Michel, N.; Fossez, K.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 4
Shell Model Description of Weakly Bound Nuclei
journal, April 2005
 Michel, N.; Nazarewicz, W.; Okołowicz, J.
 Nuclear Physics A, Vol. 752
Local chiral potentials with $\mathrm{\Delta}$ intermediate states and the structure of light nuclei
journal, November 2016
 Piarulli, M.; Girlanda, L.; Schiavilla, R.
 Physical Review C, Vol. 94, Issue 5
Coupledcluster computations of atomic nuclei
journal, September 2014
 Hagen, G.; Papenbrock, T.; HjorthJensen, M.
 Reports on Progress in Physics, Vol. 77, Issue 9
Variational multiparticlemultihole configuration mixing method applied to pairing correlations in nuclei
journal, August 2008
 Pillet, N.; Berger, J. F.; Caurier, E.
 Physical Review C, Vol. 78, Issue 2
Gamow shell model and realistic nucleonnucleon interactions
journal, June 2006
 Hagen, G.; HjorthJensen, M.; Michel, N.
 Physical Review C, Vol. 73, Issue 6
Continuum effects in neutrondripline oxygen isotopes
journal, August 2017
 Fossez, K.; Rotureau, J.; Michel, N.
 Physical Review C, Vol. 96, Issue 2
Meanfield description of groundstate properties of dripline nuclei: Pairing and continuum effects
journal, June 1996
 Dobaczewski, J.; Nazarewicz, W.; Werner, T. R.
 Physical Review C, Vol. 53, Issue 6
The shell model as a unified view of nuclear structure
journal, June 2005
 Caurier, E.; MartínezPinedo, G.; Nowacki, F.
 Reviews of Modern Physics, Vol. 77, Issue 2
Fitting theories of nuclear binding energies
journal, May 2005
 Bertsch, G. F.; Sabbey, B.; Uusnäkki, M.
 Physical Review C, Vol. 71, Issue 5
Statistical error analysis for phenomenological nucleonnucleon potentials
journal, June 2014
 Navarro Pérez, R.; Amaro, J. E.; Ruiz Arriola, E.
 Physical Review C, Vol. 89, Issue 6
Error estimates of theoretical models: a guide
journal, May 2014
 Dobaczewski, J.; Nazarewicz, W.; Reinhard, PG
 Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 7
Minimally nonlocal nucleonnucleon potentials with chiral twopion exchange including $\Delta $ resonances
journal, February 2015
 Piarulli, M.; Girlanda, L.; Schiavilla, R.
 Physical Review C, Vol. 91, Issue 2
Nuclear energy density optimization: Large deformations
journal, February 2012
 Kortelainen, M.; McDonnell, J.; Nazarewicz, W.
 Physical Review C, Vol. 85, Issue 2
Shell model in the complex energy plane
journal, October 2008
 Michel, N.; Nazarewicz, W.; Płoszajczak, M.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 1
The Elastic Scattering of Protons by Alpha Particles
journal, January 1954
 Sack, S.; Biedenharn, L. C.; Breit, G.
 Physical Review, Vol. 93, Issue 2
TwoParticle Resonant States in a ManyBody Mean Field
journal, July 2002
 Id Betan, R.; Liotta, R. J.; Sandulescu, N.
 Physical Review Letters, Vol. 89, Issue 4
Alphadeuteron model of the Li6 nucleus
journal, February 1961
 Kopaleishvili, T. I.; Vashakidze, I. Sh.; Mamasakhlisov, V. I.
 Nuclear Physics, Vol. 23
Pair correlations near the neutron drip line
journal, August 1991
 Bertsch, G. F.; Esbensen, H.
 Annals of Physics, Vol. 209, Issue 2
Gamow Shell Model Description of NeutronRich Nuclei
journal, July 2002
 Michel, N.; Nazarewicz, W.; Płoszajczak, M.
 Physical Review Letters, Vol. 89, Issue 4
Error analysis of nuclear mass fits
journal, September 2008
 Toivanen, J.; Dobaczewski, J.; Kortelainen, M.
 Physical Review C, Vol. 78, Issue 3
Living on the edge of stability, the limits of the nuclear landscape
journal, January 2013
 Forssén, C.; Hagen, G.; HjorthJensen, M.
 Physica Scripta, Vol. T152
“Sloppy” nuclear energy density functionals: Effective model reduction
journal, August 2016
 Nikšić, Tamara; Vretenar, Dario
 Physical Review C, Vol. 94, Issue 2
Protonneutron coupling in the Gamow shell model: The lithium chain
journal, December 2004
 Michel, N.; Nazarewicz, W.; Płoszajczak, M.
 Physical Review C, Vol. 70, Issue 6
New analysis method of the halo phenomenon in finite manyfermion systems: First applications to mediummass atomic nuclei
journal, May 2009
 Rotival, V.; Duguet, T.
 Physical Review C, Vol. 79, Issue 5
Chapter III. Study of NonAlphaNuclei Based on the Viewpoint of Cluster Correlations
journal, January 1980
 Furutani, Hiroshi; Kanada, Hiroyuki; Kaneko, Tsuneo
 Progress of Theoretical Physics Supplement, Vol. 68
Structure and decays of nuclear threebody systems: The Gamow coupledchannel method in Jacobi coordinates
journal, October 2017
 Wang, S. M.; Michel, N.; Nazarewicz, W.
 Physical Review C, Vol. 96, Issue 4
Nuclear energy density optimization
journal, August 2010
 Kortelainen, M.; Lesinski, T.; Moré, J.
 Physical Review C, Vol. 82, Issue 2
Lattice effective field theory for mediummass nuclei
journal, May 2014
 Lähde, Timo A.; Epelbaum, Evgeny; Krebs, Hermann
 Physics Letters B, Vol. 732
Ab initio nocore solutions for ^{6} Li
journal, May 2017
 Shin, Ik Jae; Kim, Youngman; Maris, Pieter
 Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 7
The InMedium Similarity Renormalization Group: A novel ab initio method for nuclei
journal, March 2016
 Hergert, H.; Bogner, S. K.; Morris, T. D.
 Physics Reports, Vol. 621
Theoretical aspects of science with radioactive nuclear beams
journal, September 1998
 Dobaczewski, Jacek; Nazarewicz, Witold
 Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 356, Issue 1744
Shell model in the complex energy plane and twoparticle resonances
journal, January 2003
 Id Betan, R.; Liotta, R. J.; Sandulescu, N.
 Physical Review C, Vol. 67, Issue 1
The Calculation of Errors by the Method of Least Squares
journal, April 1932
 Birge, Raymond T.
 Physical Review, Vol. 40, Issue 2
Determination of Rfunction and physicalstate parameters for n4He elastic scattering below 21 MeV
journal, September 1977
 Bond, J. E.; Firk, F. W. K.
 Nuclear Physics A, Vol. 287, Issue 2
Density matrix renormalization group approach to twofluid open manyfermion systems
journal, January 2009
 Rotureau, J.; Michel, N.; Nazarewicz, W.
 Physical Review C, Vol. 79, Issue 1
Density Matrix Renormalization Group Approach for ManyBody Open Quantum Systems
journal, September 2006
 Rotureau, J.; Michel, N.; Nazarewicz, W.
 Physical Review Letters, Vol. 97, Issue 11
Bootstrapping the statistical uncertainties of NN scattering data
journal, November 2014
 Navarro Pérez, R.; Amaro, J. E.; Ruiz Arriola, E.
 Physics Letters B, Vol. 738
Precise rootmeansquare radius of ${}^{4}\mathrm{He}$
journal, April 2008
 Sick, Ingo
 Physical Review C, Vol. 77, Issue 4
Alphadeuteron structure of the 6Li ground state
journal, March 1969
 Truoel, P.; Bierter, W.
 Physics Letters B, Vol. 29, Issue 1
Pairing and continuum effects in nuclei close to the drip line
journal, November 2001
 Grasso, M.; Sandulescu, N.; Van Giai, Nguyen
 Physical Review C, Vol. 64, Issue 6
Charge radii and neutron correlations in helium halo nuclei
journal, November 2011
 Papadimitriou, G.; Kruppa, A. T.; Michel, N.
 Physical Review C, Vol. 84, Issue 5
Unified ab initio approaches to nuclear structure and reactions
journal, April 2016
 Navrátil, Petr; Quaglioni, Sofia; Hupin, Guillaume
 Physica Scripta, Vol. 91, Issue 5
Accurate nuclear radii and binding energies from a chiral interaction
journal, May 2015
 Ekström, A.; Jansen, G. R.; Wendt, K. A.
 Physical Review C, Vol. 91, Issue 5
Singleparticle and collective motion in unbound deformed ${}^{39}\mathrm{Mg}$
journal, November 2016
 Fossez, K.; Rotureau, J.; Michel, N.
 Physical Review C, Vol. 94, Issue 5
Velocity dependence of the twonucleon interaction
journal, June 1958
 Okubo, S.; Marshak, R. E.
 Annals of Physics, Vol. 4, Issue 2
Studies in Intermediate Coupling: III The Lithium Isotopes
journal, March 1955
 Lane, A. M.
 Proceedings of the Physical Society. Section A, Vol. 68, Issue 3
Phase shifts and polarization in protonalpha scattering from 0.9 to 3.2 MeV
journal, January 1967
 Brown, Louis; Haeberli, W.; Trächslin, Walter
 Nuclear Physics A, Vol. 90, Issue 2
Uncertainty Analysis and OrderbyOrder Optimization of Chiral Nuclear Interactions
journal, February 2016
 Carlsson, B. D.; Ekström, A.; Forssén, C.
 Physical Review X, Vol. 6, Issue 1
SpinOrbit Coupling in the ProtonProton Interaction
journal, July 1957
 Gammel, J. L.; Thaler, R. M.
 Physical Review, Vol. 107, Issue 1
Quantum Monte Carlo methods for nuclear physics
journal, September 2015
 Carlson, J.; Gandolfi, S.; Pederiva, F.
 Reviews of Modern Physics, Vol. 87, Issue 3
ClusterModel Study of the T=1 States in A=4 System: 3He+p Scattering
journal, October 1979
 Furutani, H.; Horiuchi, H.; Tamagaki, R.
 Progress of Theoretical Physics, Vol. 62, Issue 4
Gamow shell model description of weakly bound nuclei and unbound nuclear states
journal, May 2003
 Michel, N.; Nazarewicz, W.; Płoszajczak, M.
 Physical Review C, Vol. 67, Issue 5
Works referencing / citing this record:
Manybody calculations with deuteron based singleparticle bases and their associated natural orbits
journal, April 2018
 Puddu, G.
 Physica Scripta, Vol. 93, Issue 6
Manybody calculations with deuteron based singleparticle bases and their associated natural orbits
journal, April 2018
 Puddu, G.
 Physica Scripta, Vol. 93, Issue 6
Twoneutron halo structure of ${}^{31}\mathrm{F}$
journal, March 2020
 Michel, N.; Li, J. G.; Xu, F. R.
 Physical Review C, Vol. 101, Issue 3