Three-cluster dynamics within an ab initio framework

Quaglioni, Sofia; Romero-Redondo, Carolina; Navratil, Petr

doi:10.1103/PhysRevC.88.034320

Title: Three-cluster dynamics within an ab initio framework

Abstract

In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a ⁴He+n+n description of ⁶He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (⁴He) polarization effects.

Authors:

Quaglioni, Sofia ^[1]; Romero-Redondo, Carolina ^[2]; Navratil, Petr ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
TRIUMF, Vancouver, BC (Canada)

Publication Date:: Thu Sep 26 00:00:00 EDT 2013

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1248289

Report Number(s):: LLNL-JRNL-641181
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: 88; 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


                    Quaglioni, Sofia, Romero-Redondo, Carolina, and Navratil, Petr. Three-cluster dynamics within an ab initio framework.  United States: N. p., 2013. 
Web.  doi:10.1103/PhysRevC.88.034320.

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                    Quaglioni, Sofia, Romero-Redondo, Carolina, & Navratil, Petr. Three-cluster dynamics within an ab initio framework.  United States.  https://doi.org/10.1103/PhysRevC.88.034320

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                    Quaglioni, Sofia, Romero-Redondo, Carolina, and Navratil, Petr. Thu .  
"Three-cluster dynamics within an ab initio framework".  United States.  https://doi.org/10.1103/PhysRevC.88.034320.  https://www.osti.gov/servlets/purl/1248289.

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@article{osti_1248289,

  title        = {Three-cluster dynamics within an ab initio framework},

  author       = {Quaglioni, Sofia and Romero-Redondo, Carolina and Navratil, Petr},

  abstractNote = {In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.},

  doi          = {10.1103/PhysRevC.88.034320},

  journal      = {Physical Review C, Nuclear Physics},

  number       = 3,

  volume       = 88,

  place        = {United States},

  year         = {Thu Sep 26 00:00:00 EDT 2013},

  month        = {Thu Sep 26 00:00:00 EDT 2013}

}

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Three-body systems with Lagrange-mesh techniques in hyperspherical coordinates journal, April 2003

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

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

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

The R -matrix theory journal, February 2010

First Direct Mass Measurement of the Two-Neutron Halo Nucleus He 6 and Improved Mass for the Four-Neutron Halo He 8 journal, January 2012

The structure of the resonating group equation journal, March 1982

Helium halo nuclei from low-momentum interactions journal, June 2009

Quantum Theory of Angular Momentum book, October 1988

6He as a Three-Cluster System: Investigation of the Ground State and Continuum 0+ States journal, September 1996

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

A microscopic three-cluster model in the hyperspherical formalism journal, August 2004

Comparative Study of Three-Body Models for Continuum States journal, January 2012

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

Structure of 6 He with an extended three-cluster model journal, March 1999

Three-body continuum states in a microscopic cluster model journal, October 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

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

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states journal, May 2008

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

Microscopic multicluster description of the neutron-rich helium isotopes journal, July 1994

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

Analysis of the R -matrix method on Lagrange meshes journal, August 1998

Detailed study of the cluster structure of light nuclei in a three-body model journal, May 1986

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

Benchmark test calculation of a four-nucleon bound state journal, August 2001

Microscopic theory of cluster radioactivity journal, February 1998

The potential harmonic expansion method journal, May 1983

Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7 He journal, March 2013

Two-neutron overlap functions for 6He from a microscopic structure model journal, December 2010

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

Measurements of Interaction Cross Sections and Nuclear Radii in the Light p -Shell Region journal, December 1985

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

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

Neutron halo nuclei journal, February 1996

A Unified Theory of the Nucleus journal, July 1977

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

Asymptotic normalization coefficients from ab initio calculations journal, April 2011

Equivalence of the Siegert-pseudostate and Lagrange-mesh R -matrix methods journal, April 2002

Ab Initio Computation of the F 17 Proton Halo State and Resonances in A = 17 Nuclei journal, May 2010

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

Algebraic model for scattering in three- s -cluster systems. I. Theoretical background journal, February 2001

Algebraic model for scattering in three- s -cluster systems. II. Resonances in the three-cluster continuum of 6 He and 6 Be journal, February 2001

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

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

Microscopic cluster description of 12 C journal, March 2012

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

Ab initio calculations of nuclear widths via an integral relation journal, October 2012

Benchmark calculation of n - 3 H and p - 3 He scattering journal, November 2011

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

Bound state properties of Borromean halo nuclei: 6He and 11Li journal, August 1993

Detailed study of the cluster structure of light nuclei in a three-body model journal, October 1990

Detailed study of the cluster structure of light nuclei in a three-body model journal, April 1984

Ab initio many-body calculations of nucleon-nucleus scattering text, January 2009

Helium halo nuclei from low-momentum interactions text, January 2009

Two-neutron overlap functions for 6He from a microscopic structure model text, January 2010

First direct mass-measurement of the two-neutron halo nucleus 6He and improved mass for the four-neutron halo 8He text, January 2011

Benchmark Test Calculation of a Four-Nucleon Bound State text, January 2001

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory text, January 2003

Three-body continuum states on a Lagrange mesh text, January 2005

Quantum Monte Carlo calculations of neutron-alpha scattering text, January 2006

Microscopic multicluster description of the neutron-rich helium isotopes text, January 1994

Nonlocalized clustering and evolution of cluster structure in nuclei journal, August 2019

Effective field theory description of halo nuclei journal, September 2017

He 6 nucleus in halo effective field theory journal, October 2014

Experimental Evidence of a Variant Neutron Spectrum from the T ( t , 2 n ) α Reaction at Center-of-Mass Energies in the Range of 16–50 keV journal, July 2018

Effective field theory description of halo nuclei text, January 2017

Microscopic Clustering in Light Nuclei text, January 2017

Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei text, January 2019

Three-body systems with Lagrange-mesh techniques in hyperspherical coordinates
journal, April 2003

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

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

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

The R -matrix theory
journal, February 2010

First Direct Mass Measurement of the Two-Neutron Halo Nucleus ${}^{6}{He}$ and Improved Mass for the Four-Neutron Halo ${}^{8}{He}$
journal, January 2012

The structure of the resonating group equation
journal, March 1982

Helium halo nuclei from low-momentum interactions
journal, June 2009

Quantum Theory of Angular Momentum
book, October 1988

6He as a Three-Cluster System: Investigation of the Ground State and Continuum 0+ States
journal, September 1996

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

A microscopic three-cluster model in the hyperspherical formalism
journal, August 2004

Comparative Study of Three-Body Models for Continuum States
journal, January 2012

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

Structure of $^{6} He$ with an extended three-cluster model
journal, March 1999

Three-body continuum states in a microscopic cluster model
journal, October 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

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

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
journal, May 2008

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

Microscopic multicluster description of the neutron-rich helium isotopes
journal, July 1994

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

Analysis of the R -matrix method on Lagrange meshes
journal, August 1998

Detailed study of the cluster structure of light nuclei in a three-body model
journal, May 1986

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

Benchmark test calculation of a four-nucleon bound state
journal, August 2001

Microscopic theory of cluster radioactivity
journal, February 1998

The potential harmonic expansion method
journal, May 1983

Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to $^{7}$ He
journal, March 2013

Two-neutron overlap functions for 6He from a microscopic structure model
journal, December 2010

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

Measurements of Interaction Cross Sections and Nuclear Radii in the Light $p$ -Shell Region
journal, December 1985

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

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

Neutron halo nuclei
journal, February 1996

A Unified Theory of the Nucleus
journal, July 1977

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

Asymptotic normalization coefficients from ab initio calculations
journal, April 2011

Equivalence of the Siegert-pseudostate and Lagrange-mesh R -matrix methods
journal, April 2002

Ab Initio Computation of the ${}^{17}F$ Proton Halo State and Resonances in $A = 17$ Nuclei
journal, May 2010

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

Algebraic model for scattering in three- $s$ -cluster systems. I. Theoretical background
journal, February 2001

Algebraic model for scattering in three- s -cluster systems. II. Resonances in the three-cluster continuum of 6 He and 6 Be
journal, February 2001

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

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

Microscopic cluster description of $^{12}$ C
journal, March 2012

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

Ab initio calculations of nuclear widths via an integral relation
journal, October 2012

Benchmark calculation of $n$ - $^{3}$ H and $p$ - $^{3}$ He scattering
journal, November 2011

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

Bound state properties of Borromean halo nuclei: 6He and 11Li
journal, August 1993

Detailed study of the cluster structure of light nuclei in a three-body model
journal, October 1990

Detailed study of the cluster structure of light nuclei in a three-body model
journal, April 1984

Ab initio many-body calculations of nucleon-nucleus scattering
text, January 2009

Helium halo nuclei from low-momentum interactions
text, January 2009

Two-neutron overlap functions for 6He from a microscopic structure model
text, January 2010

First direct mass-measurement of the two-neutron halo nucleus 6He and improved mass for the four-neutron halo 8He
text, January 2011

Benchmark Test Calculation of a Four-Nucleon Bound State
text, January 2001

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
text, January 2003

Three-body continuum states on a Lagrange mesh
text, January 2005

Quantum Monte Carlo calculations of neutron-alpha scattering
text, January 2006

Microscopic multicluster description of the neutron-rich helium isotopes
text, January 1994

Nonlocalized clustering and evolution of cluster structure in nuclei
journal, August 2019

Effective field theory description of halo nuclei
journal, September 2017

${}^{6}{He}$ nucleus in halo effective field theory
journal, October 2014

Experimental Evidence of a Variant Neutron Spectrum from the $T (t, 2 n) α$ Reaction at Center-of-Mass Energies in the Range of 16–50 keV
journal, July 2018

Effective field theory description of halo nuclei
text, January 2017

Microscopic Clustering in Light Nuclei
text, January 2017

Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei
text, January 2019