Be7 and Li7 nuclei within the no-core shell model with continuum

Vorabbi, Matteo; Navrátil, Petr; Quaglioni, Sofia; Hupin, Guillaume

doi:10.1103/PhysRevC.100.024304

Title: ${}^{7}{Be}$ and ${}^{7}{Li}$ nuclei within the no-core shell model with continuum

Abstract

The production of $^7Be$ and $^7Li$ nuclei plays an important role in primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation. The $^3He(α,γ) ^7Be$ and $^3H(α,γ) 7Li$ radiative-capture processes are important to determine the $^7Li$ abundance in the early universe and to predict the correct fraction of $pp$ -chain branches resulting in $^7Be$ versus $^8B$ neutrinos. The $^6Li(p,γ) ^7Be$ has been investigated recently hinting at a possible cross section enhancement near the threshold. The $^6Li (n,^3H) ^4He$ process can be utilized for tritium breeding in machines dedicated to fusion energy generation through the deuteron-tritium reaction, and is a neutron cross section standard used in the measurement and evaluation of fission cross sections. In this work we study the properties of $^7Be$ and $^7Li$ within the no-core shell model with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the only input, and analyze all the binary mass partitions involved in the formation of these systems. The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states and thus is well suited to investigate systems with many resonances and pronounced clustering like $^7Be$ and $^7Li$. Our calculations reproduce all the experimentally known statesmore »« less

Authors:

^[1]; Navrátil, Petr ^[1]; Quaglioni, Sofia ^[2];

^[3]

TRIUMF, Vancouver, British Columbia (Canada)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Paris-Sud, Orsay (France). Inst. of Nuclear Physics

Publication Date:: 2019-08-01

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

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1561456

Alternate Identifier(s):: OSTI ID: 1547964

Report Number(s):: LLNL-JRNL-777984
Journal ID: ISSN 2469-9985; 971810; TRN: US2000617

Grant/Contract Number:: AC52-07NA27344; SCW1158; SCW0498

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 100; Journal Issue: 2; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Vorabbi, Matteo, Navrátil, Petr, Quaglioni, Sofia, and Hupin, Guillaume. Be7 and Li7 nuclei within the no-core shell model with continuum.  United States: N. p., 2019. 
        Web.  doi:10.1103/PhysRevC.100.024304.

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                    Vorabbi, Matteo, Navrátil, Petr, Quaglioni, Sofia, & Hupin, Guillaume. Be7 and Li7 nuclei within the no-core shell model with continuum.  United States.  doi:https://doi.org/10.1103/PhysRevC.100.024304

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                    Vorabbi, Matteo, Navrátil, Petr, Quaglioni, Sofia, and Hupin, Guillaume. Thu .  
        "Be7 and Li7 nuclei within the no-core shell model with continuum".  United States.  doi:https://doi.org/10.1103/PhysRevC.100.024304.  https://www.osti.gov/servlets/purl/1561456.

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@article{osti_1561456,

  title        = {Be7 and Li7 nuclei within the no-core shell model with continuum},

  author       = {Vorabbi, Matteo and Navrátil, Petr and Quaglioni, Sofia and Hupin, Guillaume},

  abstractNote = {The production of $^7Be$ and $^7Li$ nuclei plays an important role in primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation. The $^3He(α,γ) ^7Be$ and $^3H(α,γ) 7Li$ radiative-capture processes are important to determine the $^7Li$ abundance in the early universe and to predict the correct fraction of $pp$ -chain branches resulting in $^7Be$ versus $^8B$ neutrinos. The $^6Li(p,γ) ^7Be$ has been investigated recently hinting at a possible cross section enhancement near the threshold. The $^6Li (n,^3H) ^4He$ process can be utilized for tritium breeding in machines dedicated to fusion energy generation through the deuteron-tritium reaction, and is a neutron cross section standard used in the measurement and evaluation of fission cross sections. In this work we study the properties of $^7Be$ and $^7Li$ within the no-core shell model with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the only input, and analyze all the binary mass partitions involved in the formation of these systems. The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states and thus is well suited to investigate systems with many resonances and pronounced clustering like $^7Be$ and $^7Li$. Our calculations reproduce all the experimentally known states of the two systems and provide predictions for several new resonances of both parities. Some of these new possible resonances are built on the ground states of $^6Li$ and $^6He$, and thus represent a robust prediction. We do not find any resonance in the $p + ^6Li$ mass partition near the threshold. On the other hand, in the $p + ^6He$ mass partition of $^7Li$ we observe an $S$ -wave resonance near the threshold producing a very pronounced peak in the calculated $S$ factor of the $^6He (p,γ)$ $^7Li$ radiative-capture reaction. While we do not find a resonance near the threshold in the $p + ^6Li$ channel, in the case of $^6He + p$ reaction a resonant S -wave state is predicted at a very low energy above the reaction threshold, which could be relevant for astrophysics and its implications should be investigated. We note though that this state lies above the three-body breakup threshold not included in our method and may be influenced by three-body continuum correlations.},

  doi          = {10.1103/PhysRevC.100.024304},

  journal      = {Physical Review C},

  number       = 2,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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DOI: https://doi.org/10.1103/PhysRevC.100.024304

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Journal Article Setoodehnia, K. ; Kelley, J. H. ; Marshall, C. ; ... - Physical Review C

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DOI: https://doi.org/10.1103/PhysRevC.99.055812

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Title: Be 7 and Li 7 nuclei within the no-core shell model with continuum

Abstract

Citation Formats

Astrophysical S factor of 3 He ( α , γ ) 7 Be journal, June 2013

Consistent cluster model description of the electromagnetic properties of lithium and beryllium nuclei journal, November 1986

Sharpening the Predictions of Big-Bang Nucleosynthesis journal, May 1999

Ab initio no core shell model journal, March 2013

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

Cross section of the reaction 6Li(p, γ)7Be journal, November 1979

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

Angular Distributions for 6Li(p,g)7Be journal, January 1987

New measurement of the 3 He( α , γ ) 7 Be cross section at medium energies journal, September 2012

The R -matrix theory journal, February 2010

Estimating reaction rates and uncertainties for primordial nucleosynthesis journal, May 2000

The structure of the resonating group equation journal, March 1982

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

Primordial nucleosynthesis journal, April 2016

Nuclear Charge Radii of Be 7 , 9 , 10 and the One-Neutron Halo Nucleus Be 11 journal, February 2009

LUNA: Status and prospects journal, January 2018

Stellar and Primordial Nucleosynthesis of Be 7 : Measurement of He 3 ( α , γ ) Be 7 journal, June 2009

Few-nucleon forces from chiral Lagrangians journal, June 1994

Four-nucleon force in chiral effective field theory journal, August 2006

Microscopic approach based on a multiscale algebraic version of the resonating group model for radiative capture reactions journal, December 2017

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

Table of nuclear moments journal, July 1989

The 3He(α, γ)7Be and 3He(α, γ)7Li reactions at astrophysical energies journal, December 1986

Astrophysical He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 direct capture reactions in a potential-model approach journal, March 2018

Gamow shell model description of radiative capture reactions 6 Li( p , γ ) 7 Be and 6 Li( n , γ ) 7 Li journal, March 2017

H 3 (α,γ ) 7 Li reaction at low energies journal, October 1994

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

Activation measurement of the reaction cross section at high energies journal, June 2013

Effective chiral lagrangians for nucleon-pion interactions and nuclear forces journal, September 1991

Theoretical calculation of the p − 6 Li radiative capture reaction journal, July 2019

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

Modified two-body potential approach to the peripheral direct capture astrophysical reaction and asymptotic normalization coefficients journal, January 2007

The electric moments of 7Li from coulomb scattering journal, August 1991

Nuclear forces from chiral lagrangians journal, November 1990

Cross section of He 3 ( α , γ ) Be 7 around the Be 7 proton separation threshold journal, May 2019

Nuclear charge- and magnetization-density-distribution parameters from elastic electron scattering journal, November 1974

Radiative Proton Capture on 6 He journal, July 2001

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

Constraining the 7Be(p,γ)8B S-factor with the new precise 7Be solar neutrino flux from Borexino journal, February 2018

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

A drop in the Li 6 ( p , γ ) Be 7 reaction at low energies journal, October 2013

He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 astrophysical S factors from the no-core shell model with continuum journal, June 2016

Experimental status of 7 Be production and destruction at astrophysical relevant energies journal, January 2016

Radiative capture of protons by light nuclei at low energies journal, March 1992

New Precision Measurement of the H e 3 ( H e 4 , γ ) B e 7 Cross Section journal, December 2004

Electromagnetic excitation of aligned Li 7 nuclei journal, July 1985

Astrophysical S factor of the He 3 ( α , γ ) Be 7 reaction measured at low energy via detection of prompt and delayed γ rays journal, June 2007

Nucleon-nucleon potential from an effective chiral Lagrangian journal, March 1994

Nuclear-matter distribution in the proton-rich nuclei 7Be and 8B from intermediate energy proton elastic scattering in inverse kinematics journal, September 2019

Radiative α -capture cross sections from realistic nucleon-nucleon interactions and variational Monte Carlo wave functions journal, April 2001

Three-nucleon forces from chiral effective field theory journal, December 2002

Microscopic Calculation of the He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 Capture Cross Sections Using Realistic Interactions journal, January 2011

Determination of the 3 He + α → 7 Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the 3 He( α , γ ) 7 Be astrophysical S factors to the solar energy region journal, April 2012

Energy dependence of the astrophysical S factor for the Li 6 ( p , γ ) Be 7 reaction journal, November 2004

Solar fusion cross sections. II. The p p chain and CNO cycles journal, April 2011

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

The cosmological lithium problem revisited conference, January 2016

Unified ab initio approaches to nuclear structure and reactions journal, April 2016

He 3 + He 4 → Be 7 astrophysical S factor journal, November 2007

Study of the 3 He( 4 He,?) 7 Be and 3 H( 4 He,?) 7 Li Reactions in an Extended Two-Cluster Model journal, November 2000

Flow-equations for Hamiltonians journal, January 1994

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

First measurement of the B ( E 2 ; 3 / 2 − → 1 / 2 − ) transition strength in Be 7 : Testing a b i n i t i o predictions for A = 7 nuclei journal, June 2019

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

Deuteron-induced nucleon transfer reactions within an ab initio framework: First application to p -shell nuclei journal, May 2016

Ab initio predictions for polarized deuterium-tritium thermonuclear fusion journal, January 2019

Activation Measurement of the He 3 ( α , γ ) Be 7 Cross Section at Low Energy journal, September 2006

Solar fusion cross sections journal, October 1998

Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory journal, May 2018

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

Direct-Capture Model for the He 3 ( α , γ ) Be 7 and T ( α , γ ) Li 7 Reactions journal, September 1963

Title: ${}^{7}{Be}$ and ${}^{7}{Li}$ nuclei within the no-core shell model with continuum

Astrophysical $S$ factor of $^{3}$ He ${(α, γ)}^{7}$ Be
journal, June 2013

Consistent cluster model description of the electromagnetic properties of lithium and beryllium nuclei
journal, November 1986

Sharpening the Predictions of Big-Bang Nucleosynthesis
journal, May 1999

Ab initio no core shell model
journal, March 2013

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

Cross section of the reaction 6Li(p, γ)7Be
journal, November 1979

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

Angular Distributions for 6Li(p,g)7Be
journal, January 1987

New measurement of the $^{3}$ He( $α$ , $γ$ ) $^{7}$ Be cross section at medium energies
journal, September 2012

The R -matrix theory
journal, February 2010

Estimating reaction rates and uncertainties for primordial nucleosynthesis
journal, May 2000

The structure of the resonating group equation
journal, March 1982

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

Primordial nucleosynthesis
journal, April 2016

Nuclear Charge Radii of ${}^{7, 9, 10}{Be}$ and the One-Neutron Halo Nucleus ${}^{11}{Be}$
journal, February 2009

LUNA: Status and prospects
journal, January 2018

Stellar and Primordial Nucleosynthesis of ${}^{7}{Be}$ : Measurement of ${}^{3}{He} (α, γ) {}^{7}{Be}$
journal, June 2009

Few-nucleon forces from chiral Lagrangians
journal, June 1994

Four-nucleon force in chiral effective field theory
journal, August 2006

Microscopic approach based on a multiscale algebraic version of the resonating group model for radiative capture reactions
journal, December 2017

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

Table of nuclear moments
journal, July 1989

The 3He(α, γ)7Be and 3He(α, γ)7Li reactions at astrophysical energies
journal, December 1986

Astrophysical ${}^{3}{He} (α, γ) {}^{7}{Be}$ and ${}^{3}H (α, γ) {}^{7}{Li}$ direct capture reactions in a potential-model approach
journal, March 2018

Gamow shell model description of radiative capture reactions ⁶ Li( p , γ ) ⁷ Be and ⁶ Li( n , γ ) ⁷ Li
journal, March 2017

${}^{3}H$ (α,γ $)^{7}$ Li reaction at low energies
journal, October 1994

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

Activation measurement of the reaction cross section at high energies
journal, June 2013

Effective chiral lagrangians for nucleon-pion interactions and nuclear forces
journal, September 1991

Theoretical calculation of the $p -^{6} Li$ radiative capture reaction
journal, July 2019

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

Modified two-body potential approach to the peripheral direct capture astrophysical reaction and asymptotic normalization coefficients
journal, January 2007

The electric moments of 7Li from coulomb scattering
journal, August 1991

Nuclear forces from chiral lagrangians
journal, November 1990

Cross section of ${}^{3}{He} (α, γ) {}^{7}{Be}$ around the ${}^{7}{Be}$ proton separation threshold
journal, May 2019

Nuclear charge- and magnetization-density-distribution parameters from elastic electron scattering
journal, November 1974

Radiative Proton Capture on $^{6} He$
journal, July 2001

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

Constraining the 7Be(p,γ)8B S-factor with the new precise 7Be solar neutrino flux from Borexino
journal, February 2018

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

A drop in the ${}^{6}{Li} (p, γ) {}^{7}{Be}$ reaction at low energies
journal, October 2013

${}^{3}{He} (α, γ) {}^{7}{Be}$ and ${}^{3}H (α, γ) {}^{7}{Li}$ astrophysical S factors from the no-core shell model with continuum
journal, June 2016

Experimental status of ⁷ Be production and destruction at astrophysical relevant energies
journal, January 2016

Radiative capture of protons by light nuclei at low energies
journal, March 1992

New Precision Measurement of the ${}^{3}{H e} ({}^{4}{H e}, γ) {}^{7}{B e}$ Cross Section
journal, December 2004

Electromagnetic excitation of aligned ${}^{7}{Li}$ nuclei
journal, July 1985

Astrophysical $S$ factor of the ${}^{3}{He}$ ( $α, γ$ ) ${}^{7}{Be}$ reaction measured at low energy via detection of prompt and delayed γ rays
journal, June 2007

Nucleon-nucleon potential from an effective chiral Lagrangian
journal, March 1994

Nuclear-matter distribution in the proton-rich nuclei 7Be and 8B from intermediate energy proton elastic scattering in inverse kinematics
journal, September 2019

Radiative α -capture cross sections from realistic nucleon-nucleon interactions and variational Monte Carlo wave functions
journal, April 2001

Three-nucleon forces from chiral effective field theory
journal, December 2002

Microscopic Calculation of the ${}^{3}{He} (α, γ) {}^{7}{Be}$ and ${}^{3}H (α, γ) {}^{7}{Li}$ Capture Cross Sections Using Realistic Interactions
journal, January 2011

Determination of the $^{3} He + α \to^{7}$ Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the $^{3}$ He( ${α, γ)}^{7}$ Be astrophysical $S$ factors to the solar energy region
journal, April 2012

Energy dependence of the astrophysical $S$ factor for the ${}^{6}{Li} (p, γ) {}^{7}{Be}$ reaction
journal, November 2004

Solar fusion cross sections. II. The $p p$ chain and CNO cycles
journal, April 2011

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

The cosmological lithium problem revisited
conference, January 2016

Unified ab initio approaches to nuclear structure and reactions
journal, April 2016

${}^{3}{He} + {}^{4}{He}$ $\to$ ${}^{7}{Be}$ astrophysical $S$ factor
journal, November 2007

Study of the 3 He( 4 He,?) 7 Be and 3 H( 4 He,?) 7 Li Reactions in an Extended Two-Cluster Model
journal, November 2000

Flow-equations for Hamiltonians
journal, January 1994

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

First measurement of the $B (E 2; 3 / 2^{-} \to 1 / 2^{-}$ ) transition strength in ${}^{7}{Be}$ : Testing $a b i n i t i o$ predictions for $A = 7$ nuclei
journal, June 2019

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

Deuteron-induced nucleon transfer reactions within an ab initio framework: First application to $p$ -shell nuclei
journal, May 2016

Ab initio predictions for polarized deuterium-tritium thermonuclear fusion
journal, January 2019

Activation Measurement of the ${}^{3}{He} (α, γ) {}^{7}{Be}$ Cross Section at Low Energy
journal, September 2006

Solar fusion cross sections
journal, October 1998

Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory
journal, May 2018

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

Direct-Capture Model for the ${He}^{3} (α, γ) {Be}^{7}$ and $T (α, γ) {Li}^{7}$ Reactions
journal, September 1963