Largescale exact diagonalizations reveal lowmomentum scales of nuclei
Abstract
Ab initio methods aim to solve the nuclear manybody problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as fewnucleon systems. In this paper, we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding $${10}^{10}$$ on a single compute node. This allows us to perform nocore shell model (NCSM) calculations for $$^{6}\mathrm{Li}$$ in model spaces up to $${N}_{\mathrm{max}}=22$$ and to reveal the $$^{4}\mathrm{He}$$+d halo structure of this nucleus. Still, the use of a finite harmonicoscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finitesize corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupledcluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant boundstate observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Finally, using largescale NCSM calculations we numerically verify this smallmomentum scale of finite nuclei.
 Authors:

 Chalmers Univ. of Technology, Göteborg (Sweden). Dept. of Physics
 Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Physics Division
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States); Chalmers Univ. of Technology, Göteborg (Sweden)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP); Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
 OSTI Identifier:
 1471876
 Alternate Identifier(s):
 OSTI ID: 1430150
 Grant/Contract Number:
 AC0500OR22725; FG0296ER40963; SC0008499; SC0018223; IG20125158
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; fewbody systems; nuclear manybody theory; nuclear structure & decays; ab initio calculations
Citation Formats
Forssén, C., Carlsson, B. D., Johansson, H. T., Sääf, D., Bansal, A., Hagen, G., and Papenbrock, T. Largescale exact diagonalizations reveal lowmomentum scales of nuclei. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.97.034328.
Forssén, C., Carlsson, B. D., Johansson, H. T., Sääf, D., Bansal, A., Hagen, G., & Papenbrock, T. Largescale exact diagonalizations reveal lowmomentum scales of nuclei. United States. doi:10.1103/PhysRevC.97.034328.
Forssén, C., Carlsson, B. D., Johansson, H. T., Sääf, D., Bansal, A., Hagen, G., and Papenbrock, T. Wed .
"Largescale exact diagonalizations reveal lowmomentum scales of nuclei". United States. doi:10.1103/PhysRevC.97.034328. https://www.osti.gov/servlets/purl/1471876.
@article{osti_1471876,
title = {Largescale exact diagonalizations reveal lowmomentum scales of nuclei},
author = {Forssén, C. and Carlsson, B. D. and Johansson, H. T. and Sääf, D. and Bansal, A. and Hagen, G. and Papenbrock, T.},
abstractNote = {Ab initio methods aim to solve the nuclear manybody problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as fewnucleon systems. In this paper, we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding ${10}^{10}$ on a single compute node. This allows us to perform nocore shell model (NCSM) calculations for $^{6}\mathrm{Li}$ in model spaces up to ${N}_{\mathrm{max}}=22$ and to reveal the $^{4}\mathrm{He}$+d halo structure of this nucleus. Still, the use of a finite harmonicoscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finitesize corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupledcluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant boundstate observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Finally, using largescale NCSM calculations we numerically verify this smallmomentum scale of finite nuclei.},
doi = {10.1103/PhysRevC.97.034328},
journal = {Physical Review C},
issn = {24699985},
number = 3,
volume = 97,
place = {United States},
year = {2018},
month = {3}
}
Web of Science
Works referenced in this record:
Quantum Monte Carlo calculations of nuclei with $A<~7$
journal, October 1997
 Pudliner, B. S.; Pandharipande, V. R.; Carlson, J.
 Physical Review C, Vol. 56, Issue 4
The Theory of ThreeNucleon Systems
journal, December 1974
 Kim, Y. E.; Tubis, A.
 Annual Review of Nuclear Science, Vol. 24, Issue 1
Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986
 Lüscher, M.
 Communications in Mathematical Physics, Vol. 104, Issue 2
Benchmark calculations for ${}^{3}\mathrm{H}$ , ${}^{4}\mathrm{He}$ , ${}^{16}\mathrm{O}$ , and ${}^{40}\mathrm{Ca}$ with ab initio coupledcluster theory
journal, October 2007
 Hagen, G.; Dean, D. J.; HjorthJensen, M.
 Physical Review C, Vol. 76, Issue 4
Nonrelativistic bound states in a finite volume
journal, June 2012
 König, Sebastian; Lee, Dean; Hammer, H. W.
 Annals of Physics, Vol. 327, Issue 6
Ab initio no core shell model
journal, March 2013
 Barrett, Bruce R.; Navrátil, Petr; Vary, James P.
 Progress in Particle and Nuclear Physics, Vol. 69
Improving upon CCSD(T): ΛCCSD(T). I. Potential energy surfaces
journal, January 2008
 Taube, Andrew G.; Bartlett, Rodney J.
 The Journal of Chemical Physics, Vol. 128, Issue 4
Axially deformed solution of the SkyrmeHartree–Fock–Bogoliubov equations using the transformed harmonic oscillator basis (II) hfbtho v2.00d: A new version of the program
journal, June 2013
 Stoitsov, M. V.; Schunck, N.; Kortelainen, M.
 Computer Physics Communications, Vol. 184, Issue 6
Evolving nuclear manybody forces with the similarity renormalization group
journal, March 2011
 Jurgenson, E. D.; Navrátil, P.; Furnstahl, R. J.
 Physical Review C, Vol. 83, Issue 3
Convergence in the nocore shell model with lowmomentum twonucleon interactions
journal, March 2008
 Bogner, S. K.; Furnstahl, R. J.; Maris, P.
 Nuclear Physics A, Vol. 801, Issue 12
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
Nocore shell model in an effectivefieldtheory framework
journal, September 2007
 Stetcu, I.; Barrett, B. R.; van Kolck, U.
 Physics Letters B, Vol. 653, Issue 24
Status of the Nuclear Shell Model
journal, December 1988
 Brown, B. A.; Wildenthal, B. H.
 Annual Review of Nuclear and Particle Science, Vol. 38, Issue 1
Optimized Chiral NucleonNucleon Interaction at NexttoNexttoLeading Order
journal, May 2013
 Ekström, A.; Baardsen, G.; Forssén, C.
 Physical Review Letters, Vol. 110, Issue 19
Systematic expansion for infrared oscillator basis extrapolations
journal, April 2014
 Furnstahl, R. J.; More, S. N.; Papenbrock, T.
 Physical Review C, Vol. 89, Issue 4
Nuclear Charge Radii of ${}^{9,11}\mathrm{Li}$ : The Influence of Halo Neutrons
journal, January 2006
 Sánchez, R.; Nörtershäuser, W.; Ewald, G.
 Physical Review Letters, Vol. 96, Issue 3
Asymptotic normalization parameter of the triton
journal, March 1979
 Girard, B. A.; Fuda, M. G.
 Physical Review C, Vol. 19, Issue 3
Ab initio coupledcluster approach to nuclear structure with modern nucleonnucleon interactions
journal, September 2010
 Hagen, G.; Papenbrock, T.; Dean, D. J.
 Physical Review C, Vol. 82, Issue 3
Infrared length scale and extrapolations for the nocore shell model
journal, June 2015
 Wendt, K. A.; Forssén, C.; Papenbrock, T.
 Physical Review C, Vol. 91, Issue 6
Newgeneration Monte Carlo shell model for the K computer era
journal, January 2012
 Shimizu, Noritaka; Abe, Takashi; Tsunoda, Yusuke
 Progress of Theoretical and Experimental Physics, Vol. 2012, Issue 1
Universal properties of infrared oscillator basis extrapolations
journal, April 2013
 More, S. N.; Ekström, A.; Furnstahl, R. J.
 Physical Review C, Vol. 87, Issue 4
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
Chaotic Wave Functions and Exponential Convergence of LowLying Energy Eigenvalues
journal, March 1999
 Horoi, Mihai; Volya, Alexander; Zelevinsky, Vladimir
 Physical Review Letters, Vol. 82, Issue 10
DIRHB—A relativistic selfconsistent meanfield framework for atomic nuclei
journal, June 2014
 Nikšić, T.; Paar, N.; Vretenar, D.
 Computer Physics Communications, Vol. 185, Issue 6
CoulombSturmian basis for the nuclear manybody problem
journal, September 2012
 Caprio, M. A.; Maris, P.; Vary, J. P.
 Physical Review C, Vol. 86, Issue 3
Selfconsistent Green's function method for nuclei and nuclear matter
journal, April 2004
 Dickhoff, W. H.; Barbieri, C.
 Progress in Particle and Nuclear Physics, Vol. 52, Issue 2
Convergence properties of ab initio calculations of light nuclei in a harmonic oscillator basis
journal, November 2012
 Coon, S. A.; Avetian, M. I.; Kruse, M. K. G.
 Physical Review C, Vol. 86, Issue 5
A general framework for discrete variable representation basis sets
journal, May 2002
 Littlejohn, Robert G.; Cargo, Matthew; Carrington, Tucker
 The Journal of Chemical Physics, Vol. 116, Issue 20
Manyfermion theory in expS (or coupled cluster) form
journal, February 1978
 Kümmel, H.; Lührmann, K. H.; Zabolitzky, J. G.
 Physics Reports, Vol. 36, Issue 1
Recent developments in nocore shellmodel calculations
journal, May 2009
 Navrátil, Petr; Quaglioni, Sofia; Stetcu, Ionel
 Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 8
Corrections to nuclear energies and radii in finite oscillator spaces
journal, September 2012
 Furnstahl, R. J.; Hagen, G.; Papenbrock, T.
 Physical Review C, Vol. 86, Issue 3
Infrared extrapolations for atomic nuclei
journal, February 2015
 Furnstahl, R. J.; Hagen, G.; Papenbrock, T.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
Corrections to nucleon capture cross sections computed in truncated Hilbert spaces
journal, March 2017
 Acharya, B.; Ekström, A.; Odell, D.
 Physical Review C, Vol. 95, Issue 3
Factorization in largescale manybody calculations
journal, December 2013
 Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.
 Computer Physics Communications, Vol. 184, Issue 12
Ab initio nocore full configuration calculations of light nuclei
journal, January 2009
 Maris, P.; Vary, J. P.; Shirokov, A. M.
 Physical Review C, Vol. 79, Issue 1
Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonicoscillator basis.
journal, January 2012
 Schunck, N.; Dobaczewski, J.; McDonnell, J.
 Computer Physics Communications, Vol. 183, Issue 1
Coupledcluster computations of atomic nuclei
journal, September 2014
 Hagen, G.; Papenbrock, T.; HjorthJensen, M.
 Reports on Progress in Physics, Vol. 77, Issue 9
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
Volume dependence of N body bound states
journal, April 2018
 König, Sebastian; Lee, Dean
 Physics Letters B, Vol. 779
Converging sequences in the ab initio nocore shell model
journal, February 2008
 Forssén, C.; Vary, J. P.; Caurier, E.
 Physical Review C, Vol. 77, Issue 2
Ultraviolet extrapolations in finite oscillator bases
journal, December 2014
 König, S.; Bogner, S. K.; Furnstahl, R. J.
 Physical Review C, Vol. 90, Issue 6
Infrared extrapolations of quadrupole moments and transitions
journal, April 2016
 Odell, D.; Papenbrock, T.; Platter, L.
 Physical Review C, Vol. 93, Issue 4
Electronscattering form factors for ${}^{6}\mathrm{Li}$ in the ab initio symmetryguided framework
journal, February 2015
 Dytrych, T.; Hayes, A. C.; Launey, K. D.
 Physical Review C, Vol. 91, Issue 2
Extrapolation method for the nocore shell model
journal, March 2004
 Zhan, H.; Nogga, A.; Barrett, B. R.
 Physical Review C, Vol. 69, Issue 3
Nuclear structure with accurate chiral perturbation theory nucleonnucleon potential: Application to Li6 and B10
journal, January 2004
 Navrátil, P.; Caurier, E.
 Physical Review C, Vol. 69, Issue 1
Full 0ħω shell model calculation of the binding energies of the ${1f}_{7/2}$ nuclei
journal, April 1999
 Caurier, E.; MartínezPinedo, G.; Nowacki, F.
 Physical Review C, Vol. 59, Issue 4