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

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

Abstract

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.

Authors:

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)

Publication Date:: Tue Mar 26 00:00:00 EDT 2013

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1248269

Alternate Identifier(s):: OSTI ID: 1103973

Report Number(s):: LLNL-JRNL-610077
Journal ID: ISSN 0556-2813; PRVCAN

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C, Nuclear Physics

Additional Journal Information:: Journal Volume: 87; Journal Issue: 3; Journal ID: ISSN 0556-2813

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Baroni, Simone, Navratil, Petr, and Quaglioni, Sofia. Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7He.  United States: N. p., 2013. 
Web.  doi:10.1103/PhysRevC.87.034326.

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                    Baroni, Simone, Navratil, Petr, & Quaglioni, Sofia. Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7He.  United States.  https://doi.org/10.1103/PhysRevC.87.034326

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                    Baroni, Simone, Navratil, Petr, and Quaglioni, Sofia. Tue .  
"Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7He".  United States.  https://doi.org/10.1103/PhysRevC.87.034326.  https://www.osti.gov/servlets/purl/1248269.

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@article{osti_1248269,

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

  author       = {Baroni, Simone and Navratil, Petr and Quaglioni, Sofia},

  abstractNote = {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.},

  doi          = {10.1103/PhysRevC.87.034326},

  journal      = {Physical Review C, Nuclear Physics},

  number       = 3,

  volume       = 87,

  place        = {United States},

  year         = {Tue Mar 26 00:00:00 EDT 2013},

  month        = {Tue Mar 26 00:00:00 EDT 2013}

}

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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 Navratil, Petr ; Quaglioni, Sofia ; Roth, Robert - Physical Review. C, Nuclear Physics

We combine a recently developed ab initio many-body approach capable of describing simultaneously both bound and scattering states, the ab initio no-core shell model/resonating-group method (NCSM/RGM), with an importance-truncation scheme for the cluster eigenstate basis and demonstrate its applicability to nuclei with mass numbers as high as 17. By using soft similarity renormalization-group-evolved chiral nucleon-nucleon interactions, we first calculate nucleon-{sup 4}He phase shifts, cross sections, and analyzing powers. Next, we investigate nucleon scattering on {sup 7}Li, {sup 7}Be, {sup 12}C, and {sup 16}O in coupled-channel NCSM/RGM calculations that include low-lying excited states of these nuclei. We check the convergence ofmore »« less
https://doi.org/10.1103/PHYSREVC.82.034609
Ab initio many-body calculations of deuteron-{sup 4}He scattering and {sup 6}Li states

Journal Article Navratil, Petr ; Lawrence Livermore National Laboratory, P.O. Box 808, L-414, Livermore, California 94551 ; Quaglioni, Sofia - Physical Review. C, Nuclear Physics

We extend the ab initio no-core shell model/resonating-group method (NCSM/RGM) to projectile-target binary-cluster states where the projectile is a deuteron. We discuss the formalism in detail and give algebraic expressions for the integration kernels. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we calculate deuteron-{sup 4}He scattering and investigate {sup 6}Li bound and unbound states. Virtual three-body breakup effects are obtained in an approximated way by including excited pseudostates of the deuteron in the calculation. We compare our results to experiment and to a standard NCSM calculation for {sup 6}Li.
https://doi.org/10.1103/PHYSREVC.83.044609
Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions

Journal Article Hlophe, L. ; Kravvaris, K. ; Quaglioni, S. - Physical Review. C

Deuteron-induced nuclear reactions are an essential tool for probing the structure of nuclei as well as astrophysical information such as (n, γ) cross sections. The deuteron-nucleus system is typically described within a Faddeev three-body model consisting of a neutron (n), a proton (p), and the target nucleus (A) interacting through pairwise phenomenological potentials. While Faddeev techniques enable the exact description of the three-body dynamics, their predictive power is limited in part by the omission of irreducible neutron-proton-nucleus three-body force (n–p–A 3BF). Here, our goal is to quantify systematic uncertainties stemming from the reduction of deuteron-nucleus (d + A) dynamics tomore »« less
https://doi.org/10.1103/physrevc.107.014315

Full Text Available
⁴He+n+n continuum within an ab initio framework

Journal Article Romero-Redondo, Carolina ; Quaglioni, Sofia ; Navratil, Petr ; ... - Physical Review Letters

In this study, the low-lying continuum spectrum of the ⁶He nucleus is investigated for the first time within an ab initio framework that encompasses the ⁴He+n+n three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core shell model combined with the resonating-group method, in which energy-independent nonlocal interactions among three nuclear fragments can be calculated microscopically, starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with three-body scattering boundary conditions by means of the hyperspherical-harmonics method on a Lagrange mesh. Using amore »« less
Cited by 32
https://doi.org/10.1103/PhysRevLett.113.032503

Full Text Available
Ab initio description of the exotic unbound ⁷He nucleus

Journal Article Baroni, Simone ; Navratil, Petr ; Quaglioni, Sofia - Physical Review Letters

In this study, the neutron-rich unbound ⁷He nucleus has been the subject of many experimental investigations. While the ground-state 3/2^– resonance is well established, there is a controversy concerning the excited 1/2^– resonance reported in some experiments as low lying and narrow (E_R~1 MeV, Γ≤1 MeV) while in others as very broad and located at a higher energy. This issue cannot be addressed by ab initio theoretical calculations based on traditional bound-state methods. We introduce a new unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model, a bound-state technique, with the no-coremore »« less
Cited by 93
https://doi.org/10.1103/PhysRevLett.110.022505

Full Text Available

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

Abstract

Citation Formats

Structure of A = 10 – 13 Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory journal, July 2007

Quantum Monte Carlo calculations of nuclei with A <~ 7 journal, October 1997

Doppler Shift as a Tool for Studies of Isobaric Analog States of Neutron-Rich Nuclei: Application to He 7 journal, September 2005

Effective interactions for the 1p shell journal, November 1965

Resonating-group method for nuclear many-body problems journal, November 1978

Nuclear structure in the framework of the Unitary Correlation Operator Method journal, July 2010

Ab Initio Description of the Exotic Unbound He 7 Nucleus journal, January 2013

Evolving nuclear many-body forces with the similarity renormalization group journal, March 2011

He 4 experiments can serve as a database for determining the three-nucleon force journal, April 2008

Properties of the 7He ground state from 8He neutron knockout journal, August 2009

8He–6He: a comparative study of nuclear fragmentation reactions journal, January 2001

The structure of the resonating group equation journal, March 1982

Search for excited states in He 7 with the ( d , p ) reaction journal, December 2005

Energy levels of light nuclei A=5, 6, 7 journal, September 2002

Analog States of He 7 Observed via the He 6 ( p , n ) Reaction journal, June 2004

Medium-Mass Nuclei with Normal-Ordered Chiral N N + 3 N Interactions journal, July 2012

Recoil proton tagged knockout reaction for 8He journal, January 2012

Cluster form factor calculation in the ab initio no-core shell model journal, November 2004

A Unified Theory of the Nucleus book, January 1977

Evidence for a New Low-Lying Resonance State in H 7 e journal, February 2002

Ab initio many-body calculations of nucleon-nucleus scattering journal, April 2009

Quantum Monte Carlo calculations of A = 8 nuclei journal, June 2000

Spectroscopic factor of the 7He ground state journal, February 2007

Properties of 12 C in the Ab Initio Nuclear Shell Model journal, June 2000

No-Core Shell Model Analysis of Light Nuclei journal, December 2012

Structure of He 7 by proton removal from Li 8 with the ( d , 3 He ) reaction journal, October 2008

Recent developments in no-core shell-model calculations journal, May 2009

Ab initio many-body calculations of nucleon scattering on He 4 , Li 7 , Be 7 , C 12 , and O 16 journal, September 2010

Quantum Monte Carlo Calculations of Neutron- α Scattering journal, July 2007

Quantum Monte Carlo calculations of A = 9 , 10 nuclei journal, October 2002

Continuum Effects and Three-Nucleon Forces in Neutron-Rich Oxygen Isotopes journal, June 2012

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory journal, October 2003

Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI journal, December 2001

Three-body continuum states on a Lagrange mesh journal, February 2006

Large-basis ab initio no-core shell model and its application to 12 C journal, October 2000

Search for a low-energy resonance in 7He with the 7Li(d, 2He) reaction journal, August 2006

Structure of the helium isotopes 4 He– 8 He journal, February 1997

Experimental evidence for subshell closure in He 8 and indication of a resonant state in He 7 below 1 MeV journal, April 2006

Observation of an Excited State in H 7 e with Unusual Structure journal, May 1999

Microscopic theory of cluster radioactivity journal, February 1998

Chiral effective field theory and nuclear forces journal, June 2011

Ab Initio Calculation of the Hoyle State journal, May 2011

Resonances of He 7 using the complex scaling method journal, November 2007

Similarity renormalization group for nucleon-nucleon interactions journal, June 2007

Spectroscopy of 7 He states using the ( 15 N , 17 F ) reaction on 9 Be journal, July 2001

Structure of drip-line nuclei 7,8 He via direct reactions journal, October 2006

Coupled-channel R-matrix method on a Lagrange mesh journal, September 1998

Ground state energy and width of He 7 from Li 8 proton knockout journal, October 2008

Elastic proton scattering of medium mass nuclei from coupled-cluster theory journal, August 2012

Ab initio many-body calculations of deuteron- He 4 scattering and Li 6 states journal, April 2011

Quantum Monte Carlo calculations of spectroscopic overlaps in A ⩽ 7 nuclei journal, August 2011

New Isotope of Helium: He 7 journal, April 1967

Ab Initio Many-Body Calculations of the H 3 ( d , n ) He 4 and He 3 ( d , p ) He 4 Fusion Reactions journal, January 2012

Ab Initio Many-Body Calculations of n − H 3 , n − He 4 , p − He 3 , 4 , and n − Be 10 Scattering journal, August 2008

Further Results on He 7 journal, February 1969

Nuclear Reactions for Astrophysics: Principles, Calculation and Applications of Low-Energy Reactions book, January 2009

Complex coupled-cluster approach to an ab-initio description of open quantum systems journal, November 2007

Medium-Mass Nuclei from Chiral Nucleon-Nucleon Interactions journal, August 2008

Unitary correlation operator method and similarity renormalization group: Connections and differences journal, June 2008

Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group journal, August 2009

Solving the resonating-group equation on a Lagrange mesh journal, October 2002

Ab initio shell model with a genuine three-nucleon force for the p -shell nuclei journal, September 2003

From low-momentum interactions to nuclear structure journal, July 2010

From nucleons to nuclei to fusion reactions journal, December 2012

Coupled-cluster computations of atomic nuclei journal, September 2014

Effective field theory description of halo nuclei journal, September 2017

Gamow shell model description of He 4 ( d , d ) elastic scattering reactions journal, April 2019

Structure of exotic light nuclei: Z = 2, 3, 4 journal, March 2018

Three-cluster dynamics within an ab initio framework text, January 2013

Coupled-cluster computations of atomic nuclei text, January 2013

Effective field theory description of halo nuclei text, January 2017

Microscopic Clustering in Light Nuclei text, January 2017

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

Structure of $A = 10 - 13$ Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory
journal, July 2007

Quantum Monte Carlo calculations of nuclei with $A <~ 7$
journal, October 1997

Doppler Shift as a Tool for Studies of Isobaric Analog States of Neutron-Rich Nuclei: Application to ${}^{7}{He}$
journal, September 2005

Effective interactions for the 1p shell
journal, November 1965

Resonating-group method for nuclear many-body problems
journal, November 1978

Nuclear structure in the framework of the Unitary Correlation Operator Method
journal, July 2010

Ab Initio Description of the Exotic Unbound ${}^{7}{He}$ Nucleus
journal, January 2013

Evolving nuclear many-body forces with the similarity renormalization group
journal, March 2011

${}^{4}{He}$ experiments can serve as a database for determining the three-nucleon force
journal, April 2008

Properties of the 7He ground state from 8He neutron knockout
journal, August 2009

8He–6He: a comparative study of nuclear fragmentation reactions
journal, January 2001

The structure of the resonating group equation
journal, March 1982

Search for excited states in ${}^{7}{He}$ with the ( $d, p$ ) reaction
journal, December 2005

Energy levels of light nuclei A=5, 6, 7
journal, September 2002

Analog States of ${}^{7}{He}$ Observed via the ${}^{6}{He} (p, n)$ Reaction
journal, June 2004

Medium-Mass Nuclei with Normal-Ordered Chiral $N N + 3 N$ Interactions
journal, July 2012

Recoil proton tagged knockout reaction for 8He
journal, January 2012

Cluster form factor calculation in the ab initio no-core shell model
journal, November 2004

A Unified Theory of the Nucleus
book, January 1977

Evidence for a New Low-Lying Resonance State in ${}^{7}H e$
journal, February 2002

Ab initio many-body calculations of nucleon-nucleus scattering
journal, April 2009

Quantum Monte Carlo calculations of $A = 8$ nuclei
journal, June 2000

Spectroscopic factor of the 7He ground state
journal, February 2007

Properties of $^{12} C$ in the Ab Initio Nuclear Shell Model
journal, June 2000

No-Core Shell Model Analysis of Light Nuclei
journal, December 2012

Structure of ${}^{7}{He}$ by proton removal from ${}^{8}{Li}$ with the ( $d,^{3} He$ ) reaction
journal, October 2008

Recent developments in no-core shell-model calculations
journal, May 2009

Ab initio many-body calculations of nucleon scattering on ${}^{4}{He}$ , ${}^{7}{Li}$ , ${}^{7}{Be}$ , ${}^{12}C$ , and ${}^{16}O$
journal, September 2010

Quantum Monte Carlo Calculations of Neutron- $α$ Scattering
journal, July 2007

Quantum Monte Carlo calculations of $A = 9, 10$ nuclei
journal, October 2002

Continuum Effects and Three-Nucleon Forces in Neutron-Rich Oxygen Isotopes
journal, June 2012

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory
journal, October 2003

Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI
journal, December 2001

Three-body continuum states on a Lagrange mesh
journal, February 2006

Large-basis ab initio no-core shell model and its application to $^{12} C$
journal, October 2000

Search for a low-energy resonance in 7He with the 7Li(d, 2He) reaction
journal, August 2006

Structure of the helium isotopes $^{4}$ He– $^{8}$ He
journal, February 1997

Experimental evidence for subshell closure in ${}^{8}{He}$ and indication of a resonant state in ${}^{7}{He}$ below 1 MeV
journal, April 2006

Observation of an Excited State in ${}^{7}H e$ with Unusual Structure
journal, May 1999

Microscopic theory of cluster radioactivity
journal, February 1998

Chiral effective field theory and nuclear forces
journal, June 2011

Ab Initio Calculation of the Hoyle State
journal, May 2011

Resonances of ${}^{7}{He}$ using the complex scaling method
journal, November 2007

Similarity renormalization group for nucleon-nucleon interactions
journal, June 2007

Spectroscopy of $^{7} He$ states using the $(^{15} N,^{17} F)$ reaction on $^{9} Be$
journal, July 2001

Structure of drip-line nuclei ^7,8 He via direct reactions
journal, October 2006

Coupled-channel R-matrix method on a Lagrange mesh
journal, September 1998

Ground state energy and width of ${}^{7}{He}$ from ${}^{8}{Li}$ proton knockout
journal, October 2008

Elastic proton scattering of medium mass nuclei from coupled-cluster theory
journal, August 2012

Ab initio many-body calculations of deuteron- ${}^{4}{He}$ scattering and ${}^{6}{Li}$ states
journal, April 2011

Quantum Monte Carlo calculations of spectroscopic overlaps in $A ⩽ 7$ nuclei
journal, August 2011

New Isotope of Helium: ${}^{7}{He}$
journal, April 1967

Ab Initio Many-Body Calculations of the ${}^{3}H (d, n) {}^{4}{He}$ and ${}^{3}{He} (d, p) {}^{4}{He}$ Fusion Reactions
journal, January 2012

Ab Initio Many-Body Calculations of $n − {}^{3}H$ , $n − {}^{4}{He}$ , $p − {}^{3, 4}{He}$ , and $n − {}^{10}{Be}$ Scattering
journal, August 2008

Further Results on ${}^{7}{He}$
journal, February 1969

Nuclear Reactions for Astrophysics: Principles, Calculation and Applications of Low-Energy Reactions
book, January 2009

Complex coupled-cluster approach to an ab-initio description of open quantum systems
journal, November 2007

Medium-Mass Nuclei from Chiral Nucleon-Nucleon Interactions
journal, August 2008

Unitary correlation operator method and similarity renormalization group: Connections and differences
journal, June 2008

Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
journal, August 2009

Solving the resonating-group equation on a Lagrange mesh
journal, October 2002

Ab initio shell model with a genuine three-nucleon force for the p -shell nuclei
journal, September 2003

From low-momentum interactions to nuclear structure
journal, July 2010

From nucleons to nuclei to fusion reactions
journal, December 2012

Coupled-cluster computations of atomic nuclei
journal, September 2014

Effective field theory description of halo nuclei
journal, September 2017

Gamow shell model description of ${}^{4}{He} (d, d)$ elastic scattering reactions
journal, April 2019

Structure of exotic light nuclei: Z = 2, 3, 4
journal, March 2018

Three-cluster dynamics within an ab initio framework
text, January 2013

Coupled-cluster computations of atomic nuclei
text, January 2013

Effective field theory description of halo nuclei
text, January 2017

Microscopic Clustering in Light Nuclei
text, January 2017