Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7He

Baroni, Simone; Navratil, Petr; Quaglioni, Sofia

doi:10.1103/PhysRevC.87.034326

Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to ⁷He

Journal Article · Tue Mar 26 00:00:00 EDT 2013 · Physical Review C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.87.034326· OSTI ID:1248269

Baroni, Simone ^[1]; Navratil, Petr ^[2]; Quaglioni, Sofia ^[3]

Univ. Libre de Bruxelles, Bruxelles (Belgium); TRIUMF, Vancouver, BC (Canada)
TRIUMF, Vancouver, BC (Canada); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

In this study, we introduce a unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model (NCSM), a bound-state technique, with the no-core shell model/resonating group method (NCSM/RGM), a nuclear scattering technique. This new ab initio method, no-core shell model with continuum (NCSMC), leads to convergence properties superior to either NCSM or NCSM/RGM while providing a balanced approach to different classes of states. In the NCSMC, the ansatz for the many-nucleon wave function includes (i) a square-integrable A-nucleon component expanded in a complete harmonic oscillator basis and (ii) a binary-cluster component with asymptotic boundary conditions that can properly describe weakly bound states, resonances, and scattering. The Schrödinger equation is transformed into a system of coupled-channel integral-differential equations that we solve using a modified microscopic R-matrix formalism within a Lagrange mesh basis. We demonstrate the usefulness of the approach by investigating the unbound ⁷He nucleus.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1248269

Alternate ID(s):: OSTI ID: 1103973

Report Number(s):: LLNL-JRNL--610077

Journal Information:: Physical Review C, Nuclear Physics, Journal Name: Physical Review C, Nuclear Physics Journal Issue: 3 Vol. 87; ISSN 0556-2813; ISSN PRVCAN

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (66)

A Unified Theory of the Nucleus Wildermuth, K.; Tang, Y. C. https://doi.org/10.1007/978-3-322-85255-7	book	January 1977
No-Core Shell Model Analysis of Light Nuclei Quaglioni, Sofia; Navrátil, Petr; Hupin, Guillaume Few-Body Systems, Vol. 54, Issue 7-10 https://doi.org/10.1007/s00601-012-0505-0	journal	December 2012
Effective interactions for the 1p shell Cohen, S.; Kurath, D. Nuclear Physics, Vol. 73, Issue 1 https://doi.org/10.1016/0029-5582(65)90148-3	journal	November 1965
Resonating-group method for nuclear many-body problems Tang, Y. C.; LeMere, M.; Thompsom, D. R. Physics Reports, Vol. 47, Issue 3 https://doi.org/10.1016/0370-1573(78)90175-8	journal	November 1978
The structure of the resonating group equation Fliessbach, T.; Walliser, H. Nuclear Physics A, Vol. 377, Issue 1 https://doi.org/10.1016/0375-9474(82)90322-0	journal	March 1982
Microscopic theory of cluster radioactivity Lovas, R. G.; Liotta, R. J.; Insolia, A. Physics Reports, Vol. 294, Issue 5 https://doi.org/10.1016/S0370-1573(97)00049-5	journal	February 1998
8He–6He: a comparative study of nuclear fragmentation reactions Markenroth, K.; Meister, M.; Eberlein, B. Nuclear Physics A, Vol. 679, Issue 3-4 https://doi.org/10.1016/S0375-9474(00)00372-9	journal	January 2001
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
Solving the resonating-group equation on a Lagrange mesh Hesse, M.; Roland, J.; Baye, D. Nuclear Physics A, Vol. 709, Issue 1-4 https://doi.org/10.1016/S0375-9474(02)01040-0	journal	October 2002
Coupled-channel R-matrix method on a Lagrange mesh Hesse, M.; Sparenberg, J. -M.; Van Raemdonck, F. Nuclear Physics A, Vol. 640, Issue 1 https://doi.org/10.1016/S0375-9474(98)00435-7	journal	September 1998
Three-body continuum states on a Lagrange mesh Descouvemont, P.; Tursunov, E.; Baye, D. Nuclear Physics A, Vol. 765, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2005.11.010	journal	February 2006
Core excitations in He8 and He7 Adahchour, A.; Descouvemont, P. Physics Letters B, Vol. 639, Issue 5 https://doi.org/10.1016/j.physletb.2006.05.092	journal	August 2006
Search for a low-energy resonance in 7He with the 7Li(d, 2He) reaction Ryezayeva, N.; Bäumer, C.; van den Berg, A. M. Physics Letters B, Vol. 639, Issue 6 https://doi.org/10.1016/j.physletb.2006.06.081	journal	August 2006
Spectroscopic factor of the 7He ground state Beck, F.; Frekers, D.; von Neumann-Cosel, P. Physics Letters B, Vol. 645, Issue 2-3 https://doi.org/10.1016/j.physletb.2006.12.036	journal	February 2007
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
Properties of the 7He ground state from 8He neutron knockout Aksyutina, Yu.; Johansson, H. T.; Aumann, T. Physics Letters B, Vol. 679, Issue 3 https://doi.org/10.1016/j.physletb.2009.07.044	journal	August 2009
Ab initio many-body calculation of the Be7(p,γ)B8 radiative capture Navrátil, Petr; Roth, Robert; Quaglioni, Sofia Physics Letters B, Vol. 704, Issue 5 https://doi.org/10.1016/j.physletb.2011.09.079	journal	October 2011
Recoil proton tagged knockout reaction for 8He Cao, Z. X.; Ye, Y. L.; Xiao, J. Physics Letters B, Vol. 707, Issue 1 https://doi.org/10.1016/j.physletb.2011.12.009	journal	January 2012
Chiral effective field theory and nuclear forces Machleidt, R.; Entem, D. R. Physics Reports, Vol. 503, Issue 1 https://doi.org/10.1016/j.physrep.2011.02.001	journal	June 2011
Nuclear structure in the framework of the Unitary Correlation Operator Method Roth, Robert; Neff, Thomas; Feldmeier, Hans Progress in Particle and Nuclear Physics, Vol. 65, Issue 1 https://doi.org/10.1016/j.ppnp.2010.02.003	journal	July 2010
From low-momentum interactions to nuclear structure Bogner, S. K.; Furnstahl, R. J.; Schwenk, A. Progress in Particle and Nuclear Physics, Vol. 65, Issue 1 https://doi.org/10.1016/j.ppnp.2010.03.001	journal	July 2010
Nuclear Reactions for Astrophysics: Principles, Calculation and Applications of Low-Energy Reactions Thompson, Ian J.; Nunes, Filomena M. https://doi.org/10.1017/CBO9781139152150	book	January 2009
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
From nucleons to nuclei to fusion reactions Quaglioni, S.; Navr, P.; Roth, R. Journal of Physics: Conference Series, Vol. 402 https://doi.org/10.1088/1742-6596/402/1/012037	journal	December 2012
Structure of drip-line nuclei ^7,8 He via direct reactions Lapoux, V.; Alamanos, N.; Keeley, N. Journal of Physics: Conference Series, Vol. 49 https://doi.org/10.1088/1742-6596/49/1/035	journal	October 2006
Further Results on He 7 Stokes, Richard H.; Young, P. G. Physical Review, Vol. 178, Issue 4 https://doi.org/10.1103/PhysRev.178.2024	journal	February 1969
Structure of the helium isotopes 4 He– 8 He Wurzer, Jürgen; Hofmann, Hartmut M. Physical Review C, Vol. 55, Issue 2 https://doi.org/10.1103/PhysRevC.55.688	journal	February 1997
Quantum Monte Carlo calculations of nuclei with A <~ 7 Pudliner, B. S.; Pandharipande, V. R.; Carlson, J. Physical Review C, Vol. 56, Issue 4 https://doi.org/10.1103/PhysRevC.56.1720	journal	October 1997
Quantum Monte Carlo calculations of A = 8 nuclei Wiringa, R. B.; Pieper, Steven C.; Carlson, J. Physical Review C, Vol. 62, Issue 1 https://doi.org/10.1103/PhysRevC.62.014001	journal	June 2000
Large-basis *ab initio* no-core shell model and its application to 12 C Navrátil, P.; Vary, J. P.; Barrett, B. R. Physical Review C, Vol. 62, Issue 5 https://doi.org/10.1103/PhysRevC.62.054311	journal	October 2000
Spectroscopy of 7 He states using the ( 15 N , 17 F ) reaction on 9 Be Bohlen, H. G.; Kalpakchieva, R.; Blažević, A. Physical Review C, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevC.64.024312	journal	July 2001
Quantum Monte Carlo calculations of A = 9 , 10 nuclei Pieper, Steven C.; Varga, K.; Wiringa, R. B. Physical Review C, Vol. 66, Issue 4 https://doi.org/10.1103/PhysRevC.66.044310	journal	October 2002
Ab initio shell model with a genuine three-nucleon force for the p -shell nuclei Navrátil, Petr; Ormand, W. Erich Physical Review C, Vol. 68, Issue 3 https://doi.org/10.1103/PhysRevC.68.034305	journal	September 2003
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
Cluster form factor calculation in the ab initio no-core shell model Navrátil, Petr Physical Review C, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevC.70.054324	journal	November 2004
Search for excited states in He 7 with the ( d , p ) reaction Wuosmaa, A. H.; Rehm, K. E.; Greene, J. P. Physical Review C, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevC.72.061301	journal	December 2005
Experimental evidence for subshell closure in He 8 and indication of a resonant state in He 7 below 1 MeV Skaza, F.; Lapoux, V.; Keeley, N. Physical Review C, Vol. 73, Issue 4 https://doi.org/10.1103/PhysRevC.73.044301	journal	April 2006
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
Resonances of He 7 using the complex scaling method Myo, Takayuki; Katō, Kiyoshi; Ikeda, Kiyomi Physical Review C, Vol. 76, Issue 5 https://doi.org/10.1103/PhysRevC.76.054309	journal	November 2007
He 4 experiments can serve as a database for determining the three-nucleon force Hofmann, H. M.; Hale, G. M. Physical Review C, Vol. 77, Issue 4 https://doi.org/10.1103/PhysRevC.77.044002	journal	April 2008
Unitary correlation operator method and similarity renormalization group: Connections and differences Roth, R.; Reinhardt, S.; Hergert, H. Physical Review C, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevC.77.064003	journal	June 2008
Structure of He 7 by proton removal from Li 8 with the ( d , 3 He ) reaction Wuosmaa, A. H.; Schiffer, J. P.; Rehm, K. E. Physical Review C, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevC.78.041302	journal	October 2008
Ground state energy and width of He 7 from Li 8 proton knockout Denby, D. H.; DeYoung, P. A.; Baumann, T. Physical Review C, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevC.78.044303	journal	October 2008
Ab initio many-body calculations of nucleon-nucleus scattering Quaglioni, Sofia; Navrátil, Petr Physical Review C, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevC.79.044606	journal	April 2009
Ab initio many-body calculations of nucleon scattering on He 4 , Li 7 , Be 7 , C 12 , and O 16 Navrátil, Petr; Roth, Robert; Quaglioni, Sofia Physical Review C, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevC.82.034609	journal	September 2010
Evolving nuclear many-body forces with the similarity renormalization group Jurgenson, E. D.; Navrátil, P.; Furnstahl, R. J. Physical Review C, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevC.83.034301	journal	March 2011
Ab initio many-body calculations of deuteron- He 4 scattering and Li 6 states Navrátil, Petr; Quaglioni, Sofia Physical Review C, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevC.83.044609	journal	April 2011
Quantum Monte Carlo calculations of spectroscopic overlaps in A ⩽ 7 nuclei Brida, I.; Pieper, Steven C.; Wiringa, R. B. Physical Review C, Vol. 84, Issue 2 https://doi.org/10.1103/PhysRevC.84.024319	journal	August 2011
Elastic proton scattering of medium mass nuclei from coupled-cluster theory Hagen, G.; Michel, N. Physical Review C, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevC.86.021602	journal	August 2012
Ab Initio Many-Body Calculations of n − H 3 , n − He 4 , p − He 3 , 4 , and n − Be 10 Scattering Quaglioni, Sofia; Navrátil, Petr Physical Review Letters, Vol. 101, Issue 9 https://doi.org/10.1103/PhysRevLett.101.092501	journal	August 2008
Medium-Mass Nuclei from Chiral Nucleon-Nucleon Interactions Hagen, G.; Papenbrock, T.; Dean, D. J. Physical Review Letters, Vol. 101, Issue 9 https://doi.org/10.1103/PhysRevLett.101.092502	journal	August 2008
Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group Jurgenson, E. D.; Navrátil, P.; Furnstahl, R. J. Physical Review Letters, Vol. 103, Issue 8 https://doi.org/10.1103/PhysRevLett.103.082501	journal	August 2009
Ab Initio Calculation of the Hoyle State Epelbaum, Evgeny; Krebs, Hermann; Lee, Dean Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.192501	journal	May 2011
Ab Initio Many-Body Calculations of the H 3 ( d , n ) He 4 and He 3 ( d , p ) He 4 Fusion Reactions Navrátil, Petr; Quaglioni, Sofia Physical Review Letters, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRevLett.108.042503	journal	January 2012
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
Medium-Mass Nuclei with Normal-Ordered Chiral N N + 3 N Interactions Roth, Robert; Binder, Sven; Vobig, Klaus Physical Review Letters, Vol. 109, Issue 5 https://doi.org/10.1103/PhysRevLett.109.052501	journal	July 2012
Ab Initio Description of the Exotic Unbound He 7 Nucleus Baroni, Simone; Navrátil, Petr; Quaglioni, Sofia Physical Review Letters, Vol. 110, Issue 2 https://doi.org/10.1103/PhysRevLett.110.022505	journal	January 2013
New Isotope of Helium: He 7 Stokes, Richard H.; Young, P. G. Physical Review Letters, Vol. 18, Issue 15 https://doi.org/10.1103/PhysRevLett.18.611	journal	April 1967
Observation of an Excited State in H 7 e with Unusual Structure Korsheninnikov, A. A.; Golovkov, M. S.; Ozawa, A. Physical Review Letters, Vol. 82, Issue 18 https://doi.org/10.1103/PhysRevLett.82.3581	journal	May 1999
Properties of 12 C in the Ab Initio Nuclear Shell Model Navrátil, P.; Vary, J. P.; Barrett, B. R. Physical Review Letters, Vol. 84, Issue 25 https://doi.org/10.1103/PhysRevLett.84.5728	journal	June 2000
Evidence for a New Low-Lying Resonance State in H 7 e Meister, M.; Markenroth, K.; Aleksandrov, D. Physical Review Letters, Vol. 88, Issue 10 https://doi.org/10.1103/PhysRevLett.88.102501	journal	February 2002
Analog States of He 7 Observed via the He 6 ( p , n ) Reaction Rogachev, G. V.; Boutachkov, P.; Aprahamian, A. Physical Review Letters, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevLett.92.232502	journal	June 2004
Doppler Shift as a Tool for Studies of Isobaric Analog States of Neutron-Rich Nuclei: Application to He 7 Boutachkov, P.; Rogachev, G. V.; Goldberg, V. Z. Physical Review Letters, Vol. 95, Issue 13 https://doi.org/10.1103/PhysRevLett.95.132502	journal	September 2005
Quantum Monte Carlo Calculations of Neutron- α Scattering Nollett, Kenneth M.; Pieper, Steven C.; Wiringa, R. B. Physical Review Letters, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevLett.99.022502	journal	July 2007
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
Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI Pieper, Steven C.; Wiringa, R. B. Annual Review of Nuclear and Particle Science, Vol. 51, Issue 1 https://doi.org/10.1146/annurev.nucl.51.101701.132506	journal	December 2001

Cited By (17)

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
Effective field theory description of halo nuclei Hammer, H-W; Ji, C.; Phillips, D. R. Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 10 https://doi.org/10.1088/1361-6471/aa83db	journal	September 2017
Experimental study of the low-lying negative-parity states in Be 11 using the B 12 ( d , He 3 ) Be 11 reaction Chen, J.; Auranen, K.; Avila, M. L. Physical Review C, Vol. 100, Issue 6 https://doi.org/10.1103/physrevc.100.064314	journal	December 2019
Three-cluster dynamics within an ab initio framework Quaglioni, Sofia; Romero-Redondo, Carolina; Navrátil, Petr Physical Review C, Vol. 88, Issue 3 https://doi.org/10.1103/physrevc.88.034320	journal	September 2013
Ab initio no-core Gamow shell model calculations with realistic interactions Papadimitriou, G.; Rotureau, J.; Michel, N. Physical Review C, Vol. 88, Issue 4 https://doi.org/10.1103/physrevc.88.044318	journal	October 2013
Microscopic approach based on a multiscale algebraic version of the resonating group model for radiative capture reactions Solovyev, Alexander S.; Igashov, Sergey Yu. Physical Review C, Vol. 96, Issue 6 https://doi.org/10.1103/physrevc.96.064605	journal	December 2017
Gamow shell model description of He 4 ( d , d ) elastic scattering reactions Mercenne, A.; Michel, N.; Płoszajczak, M. Physical Review C, Vol. 99, Issue 4 https://doi.org/10.1103/physrevc.99.044606	journal	April 2019
How Many-Body Correlations and α Clustering Shape He 6 Romero-Redondo, Carolina; Quaglioni, Sofia; Navrátil, Petr Physical Review Letters, Vol. 117, Issue 22 https://doi.org/10.1103/physrevlett.117.222501	journal	November 2016
Can Ab Initio Theory Explain the Phenomenon of Parity Inversion in Be 11 ? Calci, Angelo; Navrátil, Petr; Roth, Robert Physical Review Letters, Vol. 117, Issue 24 https://doi.org/10.1103/physrevlett.117.242501	journal	December 2016
Nuclear Force Imprints Revealed on the Elastic Scattering of Protons with C 10 Kumar, A.; Kanungo, R.; Calci, A. Physical Review Letters, Vol. 118, Issue 26 https://doi.org/10.1103/physrevlett.118.262502	journal	June 2017
Microscopic clustering in light nuclei Freer, Martin; Horiuchi, Hisashi; Kanada-En’yo, Yoshiko Reviews of Modern Physics, Vol. 90, Issue 3 https://doi.org/10.1103/revmodphys.90.035004	journal	August 2018
Structure of exotic light nuclei: Z = 2, 3, 4 Fortune, H. T. The European Physical Journal A, Vol. 54, Issue 3 https://doi.org/10.1140/epja/i2018-12489-2	journal	March 2018
AB INITIO NUCLEAR STRUCTURE CALCULATIONS OF p-SHELL NUCLEI WITH JISP16 Maris, Pieter; Vary, James P. International Journal of Modern Physics E, Vol. 22, Issue 07 https://doi.org/10.1142/s0218301313300166	journal	July 2013
Three-cluster dynamics within an ab initio framework Quaglioni, S.; Romero-Redondo, C.; Navrátil, P. arXiv https://doi.org/10.48550/arxiv.1307.8160	text	January 2013
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
Effective field theory description of halo nuclei Hammer, H. -W.; Ji, C.; Phillips, D. R. arXiv https://doi.org/10.48550/arxiv.1702.08605	text	January 2017
Microscopic Clustering in Light Nuclei Freer, Martin; Horiuchi, Hisashi; Kanada-En'yo, Yoshiko arXiv https://doi.org/10.48550/arxiv.1705.06192	text	January 2017

Similar Records

Ab initio many-body calculations of nucleon scattering on {sup 4}He, {sup 7}Li, {sup 7}Be, {sup 12}C, and {sup 16}O

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. C, Nuclear Physics · OSTI ID:21421039

Ab initio many-body calculations of deuteron-{sup 4}He scattering and {sup 6}Li states

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. C, Nuclear Physics · OSTI ID:21499588

Ab initio description of the exotic unbound ⁷He nucleus

Journal Article · Thu Jan 10 19:00:00 EST 2013 · Physical Review Letters · OSTI ID:1248268

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS