# Quantum Monte Carlo calculations of weak transitions in $A=6\u201310$ nuclei

## Abstract

{\it Ab initio} calculations of the Gamow-Teller (GT) matrix elements in the $$\beta$$ decays of $^6$He and $$^{10}$$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $$v_{18}$$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $$^{10}$$C data by $$\sim 2\%$$ and $$\sim 10\%$$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $$\sim 2$$--$$3\%$$ the one-body GT contributions. These findings suggest that the longstanding $$g_A$$-problem, {\it i.e.}, the systematic overprediction ($$\sim 20 \%$$ in $$A\le 18$$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Old Dominion Univ., Norfolk, VA (United States); Univ. of South Carolina, Columbia, SC (United States)
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1423779

- Alternate Identifier(s):
- OSTI ID: 1422644; OSTI ID: 1426718; OSTI ID: 1438111

- Report Number(s):
- JLAB-THY-17-2538; DOE/OR/23177-4202; arXiv:1709.03592; LA-UR-17-28128

Journal ID: ISSN 2469-9985; PRVCAN; TRN: US1801839

- Grant/Contract Number:
- SC0010300; AC05-06OR23177; AC02-06CH11357; AC52-06NA25396; AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 97; 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; Atomic and Nuclear Physics

### Citation Formats

```
Pastore, S., Baroni, A., Carlson, J., Gandolfi, S., Pieper, Steven C., Schiavilla, R., and Wiringa, R. B. Quantum Monte Carlo calculations of weak transitions in A=6–10 nuclei. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.97.022501.
```

```
Pastore, S., Baroni, A., Carlson, J., Gandolfi, S., Pieper, Steven C., Schiavilla, R., & Wiringa, R. B. Quantum Monte Carlo calculations of weak transitions in A=6–10 nuclei. United States. doi:10.1103/PhysRevC.97.022501.
```

```
Pastore, S., Baroni, A., Carlson, J., Gandolfi, S., Pieper, Steven C., Schiavilla, R., and Wiringa, R. B. Mon .
"Quantum Monte Carlo calculations of weak transitions in A=6–10 nuclei". United States. doi:10.1103/PhysRevC.97.022501. https://www.osti.gov/servlets/purl/1423779.
```

```
@article{osti_1423779,
```

title = {Quantum Monte Carlo calculations of weak transitions in A=6–10 nuclei},

author = {Pastore, S. and Baroni, A. and Carlson, J. and Gandolfi, S. and Pieper, Steven C. and Schiavilla, R. and Wiringa, R. B.},

abstractNote = {{\it Ab initio} calculations of the Gamow-Teller (GT) matrix elements in the $\beta$ decays of $^6$He and $^{10}$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $^{10}$C data by $\sim 2\%$ and $\sim 10\%$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $\sim 2$--$3\%$ the one-body GT contributions. These findings suggest that the longstanding $g_A$-problem, {\it i.e.}, the systematic overprediction ($\sim 20 \%$ in $A\le 18$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.},

doi = {10.1103/PhysRevC.97.022501},

journal = {Physical Review C},

number = 2,

volume = 97,

place = {United States},

year = {2018},

month = {2}

}

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#### Figures / Tables:

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Works referenced in this record:

##
Structure of $A=10\u201313$ Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory

journal, July 2007

- Navrátil, P.; Gueorguiev, V. G.; Vary, J. P.
- Physical Review Letters, Vol. 99, Issue 4

##
Electromagnetic and weak transitions in the seven-nucleon systems

journal, July 1983

- Walliser, H.; Liu, Q. K. K.; Kanada, H.
- Physical Review C, Vol. 28, Issue 1

##
Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

journal, November 2015

- Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian
- Physical Review Letters, Vol. 115, Issue 19

##
Accurate nucleon-nucleon potential with charge-independence breaking

journal, January 1995

- Wiringa, R. B.; Stoks, V. G. J.; Schiavilla, R.
- Physical Review C, Vol. 51, Issue 1

##
${}^{6}\mathrm{He}\hspace{0.5em}\beta $ -decay rate and the suppression of the axial constant in nuclear matter

journal, June 2009

- Vaintraub, Sergey; Barnea, Nir; Gazit, Doron
- Physical Review C, Vol. 79, Issue 6

##
Tensor Forces and the Ground-State Structure of Nuclei

journal, March 2007

- Schiavilla, R.; Wiringa, R. B.; Pieper, Steven C.
- Physical Review Letters, Vol. 98, Issue 13

##
Erratum: Nuclear axial currents in chiral effective field theory [Phys. Rev. C **93** , 015501 (2016)]

journal, May 2017

- Baroni, A.; Girlanda, L.; Pastore, S.
- Physical Review C, Vol. 95, Issue 5

##
Erratum: Tritium $\beta $ decay in chiral effective field theory [Phys. Rev. C **94** , 024003 (2016)]

journal, May 2017

- Baroni, A.; Girlanda, L.; Kievsky, A.
- Physical Review C, Vol. 95, Issue 5

##
Axial Currents in Nuclei

journal, March 1978

- Kubodera, Kuniharu; Delorme, Jean; Rho, Mannque
- Physical Review Letters, Vol. 40, Issue 12

##
Exchange currents from chiral Lagrangians

journal, March 1991

- Rho, Mannque
- Physical Review Letters, Vol. 66, Issue 10

##
Light-Nuclei Spectra from Chiral Dynamics

journal, February 2018

- Piarulli, M.; Baroni, A.; Girlanda, L.
- Physical Review Letters, Vol. 120, Issue 5

##
Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review

journal, March 2017

- Engel, Jonathan; Menéndez, Javier
- Reports on Progress in Physics, Vol. 80, Issue 4

##
Weak transitions in $A=6\mathrm{}$ and 7 nuclei

journal, April 2002

- Schiavilla, R.; Wiringa, R. B.
- Physical Review C, Vol. 65, Issue 5

##
Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths

journal, December 2014

- Ekström, A.; Jansen, G. R.; Wendt, K. A.
- Physical Review Letters, Vol. 113, Issue 26

##
Beta Decay of Carbon 10 and the Cluster Model

journal, November 1963

- Bartis, Francis J.
- Physical Review, Vol. 132, Issue 4

##
Electromagnetic reactions on light nuclei

journal, November 2014

- Bacca, Sonia; Pastore, Saori
- Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 12

##
Chiral dynamics and heavy-fermion formalism in nuclei: exchange axial currents

journal, October 1993

- Park, Tae-Sun; Min, Dong-Pil; Rho, Mannque
- Physics Reports, Vol. 233, Issue 6

##
Local chiral potentials with $\mathrm{\Delta}$ -intermediate states and the structure of light nuclei

journal, November 2016

- Piarulli, M.; Girlanda, L.; Schiavilla, R.
- Physical Review C, Vol. 94, Issue 5

##
Quantum Monte Carlo calculations of electromagnetic moments and transitions in $A\le 9$ nuclei with meson-exchange currents derived from chiral effective field theory

journal, March 2013

- Pastore, S.; Pieper, Steven C.; Schiavilla, R.
- Physical Review C, Vol. 87, Issue 3

##
Two-nucleon electromagnetic charge operator in chiral effective field theory ( $\chi $ EFT) up to one loop

journal, August 2011

- Pastore, S.; Girlanda, L.; Schiavilla, R.
- Physical Review C, Vol. 84, Issue 2

##
Overlap and Exchange Effects in Beta Decay

journal, March 1963

- Bahcall, John N.
- Physical Review, Vol. 129, Issue 6

##
Effective chiral lagrangians for nucleon-pion interactions and nuclear forces

journal, September 1991

- Weinberg, Steven
- Nuclear Physics B, Vol. 363, Issue 1

##
Chiral Lagrangian approach to exchange vector currents in nuclei

journal, January 1996

- Park, Tae-Sun; Min, Dong-Pil; Rho, Mannque
- Nuclear Physics A, Vol. 596, Issue 3-4

##
The Chiral Effective Pion-Nucleon Lagrangian of Order p4

journal, August 2000

- Fettes, Nadia; Meißner, Ulf-G.; Mojžiš, Martin
- Annals of Physics, Vol. 283, Issue 2

##
Nucleon and nucleon-pair momentum distributions in $A\le 12$ nuclei

journal, February 2014

- Wiringa, R. B.; Schiavilla, R.; Pieper, Steven C.
- Physical Review C, Vol. 89, Issue 2

##
Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including $\Delta $ resonances

journal, February 2015

- Piarulli, M.; Girlanda, L.; Schiavilla, R.
- Physical Review C, Vol. 91, Issue 2

##
Three-body interactions among nucleons and pions

journal, November 1992

- Weinberg, Steven
- Physics Letters B, Vol. 295, Issue 1-2

##
The Chiral Effective Pion–Nucleon Lagrangian of Order p4

journal, February 2001

- Fettes, Nadia; Meiβner, Ulf-G.; Mojžiš, Martin
- Annals of Physics, Vol. 288, Issue 1

##
Nuclear axial currents in chiral effective field theory

journal, January 2016

- Baroni, A.; Girlanda, L.; Pastore, S.
- Physical Review C, Vol. 93, Issue 1

##
Nuclear forces from chiral lagrangians

journal, November 1990

- Weinberg, Steven
- Physics Letters B, Vol. 251, Issue 2

##
Chiral effective field theory and nuclear forces

journal, June 2011

- Machleidt, R.; Entem, D. R.
- Physics Reports, Vol. 503, Issue 1

##
Solar neutrino experiments

journal, October 1978

- Bahcall, John N.
- Reviews of Modern Physics, Vol. 50, Issue 4

##
Nuclear axial current operators to fourth order in chiral effective field theory

journal, March 2017

- Krebs, H.; Epelbaum, E.; Meißner, U. -G.
- Annals of Physics, Vol. 378

##
Two-nucleon electromagnetic current in chiral effective field theory: One-pion exchange and short-range contributions

journal, November 2011

- Kölling, S.; Epelbaum, E.; Krebs, H.
- Physical Review C, Vol. 84, Issue 5

##
Structure and dynamics of few-nucleon systems

journal, July 1998

- Carlson, J.; Schiavilla, R.
- Reviews of Modern Physics, Vol. 70, Issue 3

##
Electromagnetic structure of few-nucleon ground states

journal, January 2016

- Marcucci, L. E.; Gross, F.; Peña, M. T.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 43, Issue 2

##
Superallowed ${0}^{+}\to {0}^{+}$ nuclear $\beta $ decays: 2014 critical survey, with precise results for ${V}_{ud}$ and CKM unitarity

journal, February 2015

- Hardy, J. C.; Towner, I. S.
- Physical Review C, Vol. 91, Issue 2

##
Quantum Monte Carlo calculations of electroweak transition matrix elements in $A=6,7$ nuclei

journal, December 2007

- Pervin, Muslema; Pieper, Steven C.; Wiringa, R. B.
- Physical Review C, Vol. 76, Issue 6

##
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

##
Precision measurement of the ${}^{6}$ He half-life and the weak axial current in nuclei

journal, September 2012

- Knecht, A.; Hong, R.; Zumwalt, D. W.
- Physical Review C, Vol. 86, Issue 3

##
Inclusive neutrino scattering off the deuteron from threshold to GeV energies

journal, September 2012

- Shen, G.; Marcucci, L. E.; Carlson, J.
- Physical Review C, Vol. 86, Issue 3

##
Parameter-free effective field theory calculation for the solar proton-fusion and hep processes

journal, May 2003

- Park, T. -S.; Marcucci, L. E.; Schiavilla, R.
- Physical Review C, Vol. 67, Issue 5

##
Tritium $\beta $ decay in chiral effective field theory

journal, August 2016

- Baroni, A.; Girlanda, L.; Kievsky, A.
- Physical Review C, Vol. 94, Issue 2

##
Gamow-Teller beta-decay rates for *A* ≤18 nuclei

journal, January 1993

- Chou, W. -T.; Warburton, E. K.; Brown, B. A.
- Physical Review C, Vol. 47, Issue 1

##
Quantum Monte Carlo Calculations of $\mathit{A}\le 6$ Nuclei

journal, May 1995

- Pudliner, B. S.; Pandharipande, V. R.; Carlson, J.
- Physical Review Letters, Vol. 74, Issue 22

##
6He β-decay from a three-body model of the A=6 system

journal, April 1978

- Parke, W. C.; Ghovanlou, A.; Noguchi, C. T.
- Physics Letters B, Vol. 74, Issue 3

##
Quantum Monte Carlo methods for nuclear physics

journal, September 2015

- Carlson, J.; Gandolfi, S.; Pederiva, F.
- Reviews of Modern Physics, Vol. 87, Issue 3

##
*Ab initio* shell model with a genuine three-nucleon force for the *p* -shell nuclei

journal, September 2003

- Navrátil, Petr; Ormand, W. Erich
- Physical Review C, Vol. 68, Issue 3

##
Erratum: Nuclear axial currents in chiral effective field theory [Phys. Rev. C **93** , 015501 (2016)]

journal, April 2016

- Baroni, A.; Girlanda, L.; Pastore, S.
- Physical Review C, Vol. 93, Issue 4

##
Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation

journal, October 2009

- Kölling, S.; Epelbaum, E.; Krebs, H.
- Physical Review C, Vol. 80, Issue 4

##
Modern theories of low-energy astrophysical reactions

journal, October 2006

- Marcucci, L. E.; Nollett, Kenneth M.; Schiavilla, R.
- Nuclear Physics A, Vol. 777

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*