${}^{7}\mathrm{Be}$ and ${}^{7}\mathrm{Li}$ nuclei within the nocore 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 $^3H(α,γ) 7Li$ radiativecapture 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 deuterontritium 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 nocore shell model with continuum (NCSMC) method, using chiral nucleonnucleon 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 »
 Authors:

 TRIUMF, Vancouver, British Columbia (Canada)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Univ. of ParisSud, Orsay (France). Inst. of Nuclear Physics
 Publication Date:
 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):
 LLNLJRNL777984
Journal ID: ISSN 24699985; 971810; TRN: US2000617
 Grant/Contract Number:
 AC5207NA27344; SCW1158; SCW0498
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 2; Journal ID: ISSN 24699985
 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 nocore shell model with continuum. United States: N. p., 2019.
Web. doi:10.1103/PhysRevC.100.024304.
Vorabbi, Matteo, Navrátil, Petr, Quaglioni, Sofia, & Hupin, Guillaume. Be7 and Li7 nuclei within the nocore shell model with continuum. United States. https://doi.org/10.1103/PhysRevC.100.024304
Vorabbi, Matteo, Navrátil, Petr, Quaglioni, Sofia, and Hupin, Guillaume. Thu .
"Be7 and Li7 nuclei within the nocore shell model with continuum". United States. https://doi.org/10.1103/PhysRevC.100.024304. https://www.osti.gov/servlets/purl/1561456.
@article{osti_1561456,
title = {Be7 and Li7 nuclei within the nocore 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 $^3H(α,γ) 7Li$ radiativecapture 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 deuterontritium 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 nocore shell model with continuum (NCSMC) method, using chiral nucleonnucleon 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 $^6He (p,γ)$ $^7Li$ radiativecapture 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 threebody breakup threshold not included in our method and may be influenced by threebody continuum correlations.},
doi = {10.1103/PhysRevC.100.024304},
journal = {Physical Review C},
number = 2,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Astrophysical $S$ factor of ${}^{3}$ He ${(\alpha ,\gamma )}^{7}$ Be
journal, June 2013
 Kontos, A.; Uberseder, E.; deBoer, R.
 Physical Review C, Vol. 87, Issue 6
Consistent cluster model description of the electromagnetic properties of lithium and beryllium nuclei
journal, November 1986
 Mertelmeier, T.; Hofmann, H. M.
 Nuclear Physics A, Vol. 459, Issue 2
Sharpening the Predictions of BigBang Nucleosynthesis
journal, May 1999
 Burles, Scott; Nollett, Kenneth M.; Truran, James W.
 Physical Review Letters, Vol. 82, Issue 21
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
Resonatinggroup method for nuclear manybody problems
journal, November 1978
 Tang, Y. C.; LeMere, M.; Thompsom, D. R.
 Physics Reports, Vol. 47, Issue 3
Cross section of the reaction 6Li(p, γ)7Be
journal, November 1979
 Switkowski, Z. E.; Heggie, J. C. P.; Kennedy, D. L.
 Nuclear Physics A, Vol. 331, Issue 1
${}^{4}\mathrm{He}$ experiments can serve as a database for determining the threenucleon force
journal, April 2008
 Hofmann, H. M.; Hale, G. M.
 Physical Review C, Vol. 77, Issue 4
Angular Distributions for 6Li(p,g)7Be
journal, January 1987
 Tingwell, Ciw; King, Jd; Sargood, Dg
 Australian Journal of Physics, Vol. 40, Issue 3
New measurement of the ${}^{3}$ He( $\alpha $ , $\gamma $ ) ${}^{7}$ Be cross section at medium energies
journal, September 2012
 CarmonaGallardo, M.; Nara Singh, B. S.; Borge, M. J. G.
 Physical Review C, Vol. 86, Issue 3
The R matrix theory
journal, February 2010
 Descouvemont, P.; Baye, D.
 Reports on Progress in Physics, Vol. 73, Issue 3
Estimating reaction rates and uncertainties for primordial nucleosynthesis
journal, May 2000
 Nollett, Kenneth M.; Burles, Scott
 Physical Review D, Vol. 61, Issue 12
The structure of the resonating group equation
journal, March 1982
 Fliessbach, T.; Walliser, H.
 Nuclear Physics A, Vol. 377, Issue 1
Energy levels of light nuclei A=5, 6, 7
journal, September 2002
 Tilley, D. R.; Cheves, C. M.; Godwin, J. L.
 Nuclear Physics A, Vol. 708, Issue 12
Primordial nucleosynthesis
journal, April 2016
 Gustavino, C.; Anders, M.; Bemmerer, D.
 The European Physical Journal A, Vol. 52, Issue 4
Nuclear Charge Radii of ${}^{7,9,10}\mathrm{Be}$ and the OneNeutron Halo Nucleus ${}^{11}\mathrm{Be}$
journal, February 2009
 Nörtershäuser, W.; Tiedemann, D.; Žáková, M.
 Physical Review Letters, Vol. 102, Issue 6
LUNA: Status and prospects
journal, January 2018
 Broggini, C.; Bemmerer, D.; Caciolli, A.
 Progress in Particle and Nuclear Physics, Vol. 98
Stellar and Primordial Nucleosynthesis of ${}^{7}\mathrm{Be}$ : Measurement of ${}^{3}\mathrm{He}(\alpha ,\gamma ){}^{7}\mathrm{Be}$
journal, June 2009
 Di Leva, A.; Gialanella, L.; Kunz, R.
 Physical Review Letters, Vol. 102, Issue 23
Fewnucleon forces from chiral Lagrangians
journal, June 1994
 van Kolck, U.
 Physical Review C, Vol. 49, Issue 6
Fournucleon force in chiral effective field theory
journal, August 2006
 Epelbaum, E.
 Physics Letters B, Vol. 639, Issue 5
Microscopic approach based on a multiscale algebraic version of the resonating group model for radiative capture reactions
journal, December 2017
 Solovyev, Alexander S.; Igashov, Sergey Yu.
 Physical Review C, Vol. 96, Issue 6
Properties of ${}^{12}C$ in the Ab Initio Nuclear Shell Model
journal, June 2000
 Navrátil, P.; Vary, J. P.; Barrett, B. R.
 Physical Review Letters, Vol. 84, Issue 25
Table of nuclear moments
journal, July 1989
 Raghavan, Pramila
 Atomic Data and Nuclear Data Tables, Vol. 42, Issue 2
The 3He(α, γ)7Be and 3He(α, γ)7Li reactions at astrophysical energies
journal, December 1986
 Kajino, Toshitaka
 Nuclear Physics A, Vol. 460, Issue 3
Astrophysical ${}^{3}\mathrm{He}(\alpha ,\gamma ){}^{7}\mathrm{Be}$ and ${}^{3}\mathrm{H}(\alpha ,\gamma ){}^{7}\mathrm{Li}$ direct capture reactions in a potentialmodel approach
journal, March 2018
 Tursunov, E. M.; Turakulov, S. A.; Kadyrov, A. S.
 Physical Review C, Vol. 97, Issue 3
Gamow shell model description of radiative capture reactions ^{6} Li( p , γ ) ^{7} Be and ^{6} Li( n , γ ) ^{7} Li
journal, March 2017
 Dong, G. X.; Michel, N.; Fossez, K.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 4
${}_{}{}^{3}{}_{}{}^{}\mathrm{H}$ (α,γ ${)}^{7}$ Li reaction at low energies
journal, October 1994
 Brune, C. R.; Kavanagh, R. W.; Rolfs, C.
 Physical Review C, Vol. 50, Issue 4
Accurate chargedependent nucleonnucleon potential at fourth order of chiral perturbation theory
journal, October 2003
 Entem, D. R.; Machleidt, R.
 Physical Review C, Vol. 68, Issue 4
Activation measurement of the reaction cross section at high energies
journal, June 2013
 Bordeanu, C.; Gyürky, Gy.; Halász, Z.
 Nuclear Physics A, Vol. 908
Effective chiral lagrangians for nucleonpion interactions and nuclear forces
journal, September 1991
 Weinberg, Steven
 Nuclear Physics B, Vol. 363, Issue 1
Theoretical calculation of the $p{}^{6}\mathrm{Li}$ radiative capture reaction
journal, July 2019
 Gnech, Alex; Marcucci, Laura Elisa
 Nuclear Physics A, Vol. 987
Largebasis ab initio nocore shell model and its application to ${}^{12}\mathbf{C}$
journal, October 2000
 Navrátil, P.; Vary, J. P.; Barrett, B. R.
 Physical Review C, Vol. 62, Issue 5
Modified twobody potential approach to the peripheral direct capture astrophysical reaction and asymptotic normalization coefficients
journal, January 2007
 Igamov, S. B.; Yarmukhamedov, R.
 Nuclear Physics A, Vol. 781, Issue 12
The electric moments of 7Li from coulomb scattering
journal, August 1991
 Voelk, H. G.; Fick, D.
 Nuclear Physics A, Vol. 530, Issue 2
Nuclear forces from chiral lagrangians
journal, November 1990
 Weinberg, Steven
 Physics Letters B, Vol. 251, Issue 2
Cross section of ${}^{3}\mathrm{He}(\alpha ,\gamma ){}^{7}\mathrm{Be}$ around the ${}^{7}\mathrm{Be}$ proton separation threshold
journal, May 2019
 Szücs, T.; Kiss, G. G.; Gyürky, Gy.
 Physical Review C, Vol. 99, Issue 5
Nuclear charge and magnetizationdensitydistribution parameters from elastic electron scattering
journal, November 1974
 De Jager, C. W.; De Vries, H.; De Vries, C.
 Atomic Data and Nuclear Data Tables, Vol. 14, Issue 56
Radiative Proton Capture on ${}^{6}\mathrm{He}$
journal, July 2001
 Sauvan, E.; Marqués, F. M.; Wilschut, H. W.
 Physical Review Letters, Vol. 87, Issue 4
Similarity renormalization group for nucleonnucleon interactions
journal, June 2007
 Bogner, S. K.; Furnstahl, R. J.; Perry, R. J.
 Physical Review C, Vol. 75, Issue 6
Constraining the 7Be(p,γ)8B Sfactor with the new precise 7Be solar neutrino flux from Borexino
journal, February 2018
 Takács, M. P.; Bemmerer, D.; Junghans, A. R.
 Nuclear Physics A, Vol. 970
Coupledchannel Rmatrix method on a Lagrange mesh
journal, September 1998
 Hesse, M.; Sparenberg, J. M.; Van Raemdonck, F.
 Nuclear Physics A, Vol. 640, Issue 1
A drop in the ${}^{6}\mathrm{Li}(p,\gamma ){}^{7}\mathrm{Be}$ reaction at low energies
journal, October 2013
 He, J. J.; Chen, S. Z.; Rolfs, C. E.
 Physics Letters B, Vol. 725, Issue 45
${}^{3}\mathrm{He}(\alpha ,\gamma ){}^{7}\mathrm{Be}$ and ${}^{3}\mathrm{H}(\alpha ,\gamma ){}^{7}\mathrm{Li}$ astrophysical S factors from the nocore shell model with continuum
journal, June 2016
 DohetEraly, Jérémy; Navrátil, Petr; Quaglioni, Sofia
 Physics Letters B, Vol. 757
Experimental status of ^{7} Be production and destruction at astrophysical relevant energies
journal, January 2016
 Leva, A. Di; Gialanella, L.; Strieder, F.
 Journal of Physics: Conference Series, Vol. 665
Radiative capture of protons by light nuclei at low energies
journal, March 1992
 Cecil, F. E.; Ferg, D.; Liu, H.
 Nuclear Physics A, Vol. 539, Issue 1
New Precision Measurement of the ${}^{3}\mathrm{H}\mathrm{e}({}^{4}\mathrm{H}\mathrm{e},\gamma )\text{\hspace{0.17em}}{}^{7}\mathrm{B}\mathrm{e}$ Cross Section
journal, December 2004
 Singh, B. S. Nara; Hass, M.; NirEl, Y.
 Physical Review Letters, Vol. 93, Issue 26
Electromagnetic excitation of aligned ${}_{}{}^{7}{}_{}{}^{}\mathrm{Li}$ nuclei
journal, July 1985
 Weller, A.; Egelhof, P.; Čaplar, R.
 Physical Review Letters, Vol. 55, Issue 5
Astrophysical $S$ factor of the ${}^{3}\mathrm{He}$ ( $\alpha ,\gamma $ ) ${}^{7}\mathrm{Be}$ reaction measured at low energy via detection of prompt and delayed γ rays
journal, June 2007
 Confortola, F.; Bemmerer, D.; Costantini, H.
 Physical Review C, Vol. 75, Issue 6
Nucleonnucleon potential from an effective chiral Lagrangian
journal, March 1994
 Ordóñez, C.; Ray, L.; van Kolck, U.
 Physical Review Letters, Vol. 72, Issue 13
Nuclearmatter distribution in the protonrich nuclei 7Be and 8B from intermediate energy proton elastic scattering in inverse kinematics
journal, September 2019
 Dobrovolsky, A. V.; Korolev, G. A.; Inglessi, A. G.
 Nuclear Physics A, Vol. 989
Radiative α capture cross sections from realistic nucleonnucleon interactions and variational Monte Carlo wave functions
journal, April 2001
 Nollett, Kenneth M.
 Physical Review C, Vol. 63, Issue 5
Threenucleon forces from chiral effective field theory
journal, December 2002
 Epelbaum, E.; Nogga, A.; Glöckle, W.
 Physical Review C, Vol. 66, Issue 6
Microscopic Calculation of the ${}^{3}\mathrm{He}(\alpha ,\gamma ){}^{7}\mathrm{Be}$ and ${}^{3}\mathbf{H}(\alpha ,\gamma ){}^{7}\mathrm{Li}$ Capture Cross Sections Using Realistic Interactions
journal, January 2011
 Neff, Thomas
 Physical Review Letters, Vol. 106, Issue 4
Determination of the ${}^{\mathbf{3}}\mathrm{He}+\alpha \to {}^{7}$ Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the ${}^{\mathbf{3}}$ He( ${\mathit{\alpha},\mathbf{\gamma})}^{\mathbf{7}}$ Be astrophysical $\mathit{S}$ factors to the solar energy region
journal, April 2012
 Tursunmahatov, Q. I.; Yarmukhamedov, R.
 Physical Review C, Vol. 85, Issue 4
Energy dependence of the astrophysical $S$ factor for the ${}^{6}\mathrm{Li}\left(p,\gamma \right){}^{7}\mathrm{Be}$ reaction
journal, November 2004
 Prior, R. M.; Spraker, M. C.; Amthor, A. M.
 Physical Review C, Vol. 70, Issue 5
Solar fusion cross sections. II. The $pp$ chain and CNO cycles
journal, April 2011
 Adelberger, E. G.; García, A.; Robertson, R. G. Hamish
 Reviews of Modern Physics, Vol. 83, Issue 1
Unitary correlation operator method and similarity renormalization group: Connections and differences
journal, June 2008
 Roth, R.; Reinhardt, S.; Hergert, H.
 Physical Review C, Vol. 77, Issue 6
The cosmological lithium problem revisited
conference, January 2016
 Bertulani, C. A.; Mukhamedzhanov, A. M.
 THERMOPHYSICS 2016: 21st International Meeting, AIP Conference Proceedings
Unified ab initio approaches to nuclear structure and reactions
journal, April 2016
 Navrátil, Petr; Quaglioni, Sofia; Hupin, Guillaume
 Physica Scripta, Vol. 91, Issue 5
${}^{3}\mathrm{He}+{}^{4}\mathrm{He}$ $\to $ ${}^{7}\mathrm{Be}$ astrophysical $S$ factor
journal, November 2007
 Brown, T. A. D.; Bordeanu, C.; Snover, K. A.
 Physical Review C, Vol. 76, Issue 5
Study of the 3 He( 4 He,?) 7 Be and 3 H( 4 He,?) 7 Li Reactions in an Extended TwoCluster Model
journal, November 2000
 Cs�t�, A.; Langanke, K.
 FewBody Systems, Vol. 29, Issue 13
Flowequations for Hamiltonians
journal, January 1994
 Wegner, Franz
 Annalen der Physik, Vol. 506, Issue 2
Evolution of Nuclear ManyBody Forces with the Similarity Renormalization Group
journal, August 2009
 Jurgenson, E. D.; Navrátil, P.; Furnstahl, R. J.
 Physical Review Letters, Vol. 103, Issue 8
First measurement of the $B(E2;3/{2}^{}\phantom{\rule{4pt}{0ex}}\to 1/{2}^{}$ ) transition strength in ${}^{7}\mathrm{Be}$ : Testing $ab\phantom{\rule{4pt}{0ex}}initio$ predictions for $A=7$ nuclei
journal, June 2019
 Henderson, S. L.; Ahn, T.; Caprio, M. A.
 Physical Review C, Vol. 99, Issue 6
Solving the resonatinggroup equation on a Lagrange mesh
journal, October 2002
 Hesse, M.; Roland, J.; Baye, D.
 Nuclear Physics A, Vol. 709, Issue 14
Deuteroninduced nucleon transfer reactions within an ab initio framework: First application to $p$ shell nuclei
journal, May 2016
 Raimondi, Francesco; Hupin, Guillaume; Navrátil, Petr
 Physical Review C, Vol. 93, Issue 5
Ab initio predictions for polarized deuteriumtritium thermonuclear fusion
journal, January 2019
 Hupin, Guillaume; Quaglioni, Sofia; Navrátil, Petr
 Nature Communications, Vol. 10, Issue 1
Activation Measurement of the ${}^{3}\mathrm{He}(\alpha ,\gamma ){}^{7}\mathrm{Be}$ Cross Section at Low Energy
journal, September 2006
 Bemmerer, D.; Confortola, F.; Costantini, H.
 Physical Review Letters, Vol. 97, Issue 12
Solar fusion cross sections
journal, October 1998
 Adelberger, Eric G.; Austin, Sam M.; Bahcall, John N.
 Reviews of Modern Physics, Vol. 70, Issue 4
Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory
journal, May 2018
 Higa, Renato; Rupak, Gautam; Vaghani, Akshay
 The European Physical Journal A, Vol. 54, Issue 5
From lowmomentum interactions to nuclear structure
journal, July 2010
 Bogner, S. K.; Furnstahl, R. J.; Schwenk, A.
 Progress in Particle and Nuclear Physics, Vol. 65, Issue 1
DirectCapture Model for the ${\mathrm{He}}^{3}(\alpha ,\gamma ){\mathrm{Be}}^{7}$ and $\mathrm{T}(\alpha ,\gamma ){\mathrm{Li}}^{7}$ Reactions
journal, September 1963
 Tombrello, T. A.; Parker, P. D.
 Physical Review, Vol. 131, Issue 6
Solar fusion cross sections
text, January 1998
 Gilles, Bogaert,; A., Duba, Charles; M., Heeger, Karsten
 The University of North Carolina at Chapel Hill University Libraries
Primordial Nucleosynthesis
journal, January 2016
 Coc, A.
 Journal of Physics: Conference Series, Vol. 665
Radiative Proton Capture on 6He
text, January 2001
 Angélique, J. C.; Marqués, F. M.; Orr, N. A.
 The American Physical Society
From lowmomentum interactions to nuclear structure
text, January 2009
 Bogner, S. K.; Furnstahl, R. J.; Schwenk, A.
 arXiv
The Cosmological Lithium Problem Revisited
text, January 2016
 Bertulani, C. A.; Mukhamedzhanov, A. M.
 arXiv
Nuclearmatter distribution in the protonrich nuclei $^7$Be and $^8$B from intermediate energy proton elastic scattering in inverse kinematics
text, January 2019
 Dobrovolsky, A. V.; Korolev, G. A.; Inglessi, A. G.
 arXiv
ThreeNucleon Forces from Chiral Effective Field Theory
text, January 2002
 Epelbaum, E.; Nogga, A.; Glöckle, W.
 arXiv
Accurate ChargeDependent NucleonNucleon Potential at Fourth Order of Chiral Perturbation Theory
text, January 2003
 Entem, D. R.; Machleidt, R.
 arXiv
Figures / Tables found in this record: