Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions
Abstract
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 to a picture of three pointlike nuclear clusters interacting via pairwise nucleon-nucleus forces, using as testing grounds d + α scattering and the 6Li ground state. We particularly focus on quantifying uncertainties arising from the full antisymmetrization of the (A + 2)-body system with the target nucleus fixed in its ground state. We adopt the ab initio no-core shell model coupled with the resonating group method (NCSM/RGM) to compute microscopic n–α and p–α interactions, and use them in a three-body description of the d + α system by means of momentum-space Faddeev-type equations. Simultaneously, we also carry out ab initio calculationsmore »
- Authors:
-
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 2005064
- Report Number(s):
- LLNL-JRNL-835853
Journal ID: ISSN 2469-9985; 1054544; TRN: US2405742
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. C
- Additional Journal Information:
- Journal Volume: 107; Journal Issue: 1; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; few-body systems; nuclear reactions; nuclear structure & decays
Citation Formats
Hlophe, L., Kravvaris, K., and Quaglioni, S. Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions. United States: N. p., 2023.
Web. doi:10.1103/physrevc.107.014315.
Hlophe, L., Kravvaris, K., & Quaglioni, S. Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions. United States. https://doi.org/10.1103/physrevc.107.014315
Hlophe, L., Kravvaris, K., and Quaglioni, S. Fri .
"Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions". United States. https://doi.org/10.1103/physrevc.107.014315. https://www.osti.gov/servlets/purl/2005064.
@article{osti_2005064,
title = {Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions},
author = {Hlophe, L. and Kravvaris, K. and Quaglioni, S.},
abstractNote = {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 to a picture of three pointlike nuclear clusters interacting via pairwise nucleon-nucleus forces, using as testing grounds d + α scattering and the 6Li ground state. We particularly focus on quantifying uncertainties arising from the full antisymmetrization of the (A + 2)-body system with the target nucleus fixed in its ground state. We adopt the ab initio no-core shell model coupled with the resonating group method (NCSM/RGM) to compute microscopic n–α and p–α interactions, and use them in a three-body description of the d + α system by means of momentum-space Faddeev-type equations. Simultaneously, we also carry out ab initio calculations of d + α scattering and 6Li ground state by means of six-body NCSM/RGM calculations to serve as a benchmark for the three-body model predictions given by the Faddeev calculations. By comparing the Faddeev and NCSM/RGM results, we show that the irreducible n–p–α 3BF has a non-negligible effect on bound state and scattering observables alike. Specifically, the Faddeev approach yields a 6Li ground state that is approximately 600 keV shallower than the one obtained with the NCSM/RGM. Additionally, the Faddeev calculations for d + α scattering yield a 3+ resonance that is located approximately 400 keV higher in energy compared to the NCSM/RGM result. The shape of the d + α angular distributions computed using the two approaches also differ, owing to the discrepancy in the predictions of the 3+ resonance energy. The Faddeev three-body model predictions for d + α scattering and 6Li using microscopic n–α and p–α potentials differ from those computed microscopically with the NCSM/RGM. These discrepancies are due to the n–p–α 3BF, which arises from two-nucleon exchange terms in the microscopic d–α interaction and are not accounted for in the three-body model Faddeev calculations. This study lays the foundation for future parametrizations of the 3BF due to Pauli exclusion principle effects in improved three-body calculations of deuteron-induced reactions.},
doi = {10.1103/physrevc.107.014315},
journal = {Physical Review. C},
number = 1,
volume = 107,
place = {United States},
year = {Fri Jan 20 00:00:00 EST 2023},
month = {Fri Jan 20 00:00:00 EST 2023}
}
Works referenced in this record:
Generalized Faddeev equations in the Alt-Grassberger-Sandhas form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction
journal, September 2012
- Mukhamedzhanov, A. M.; Eremenko, V.; Sattarov, A. I.
- Physical Review C, Vol. 86, Issue 3
Three-nucleon observables and the low-energy behavior of tripletP -wave nucleon-nucleon interactions
journal, March 2008
- Doleschall, P.
- Physical Review C, Vol. 77, Issue 3
The bonn meson-exchange model for the nucleon—nucleon interaction
journal, May 1987
- Machleidt, R.; Holinde, K.; Elster, Ch.
- Physics Reports, Vol. 149, Issue 1
The Formal Theory of Scattering
journal, July 1953
- Gell-Mann, M.; Goldberger, M. L.
- Physical Review, Vol. 91, Issue 2
Testing the Perey effect
journal, March 2014
- Titus, L. J.; Nunes, F. M.
- Physical Review C, Vol. 89, Issue 3
Separable representation of energy-dependent optical potentials
journal, March 2016
- Hlophe, L.; Elster, Ch.
- Physical Review C, Vol. 93, Issue 3
The Optical Model and Its Justification
journal, December 1958
- Feshbach, H.
- Annual Review of Nuclear Science, Vol. 8, Issue 1
Momentum space integral equations for three charged particles. II. Diagonal kernels
journal, March 2001
- Mukhamedzhanov, A. M.; Alt, E. O.; Avakov, G. V.
- Physical Review C, Vol. 63, Issue 4
Similarity renormalization group for nucleon-nucleon interactions
journal, June 2007
- Bogner, S. K.; Furnstahl, R. J.; Perry, R. J.
- Physical Review C, Vol. 75, Issue 6
Few-body universality in the deuteron- system
journal, November 2018
- Lei, Jin; Hlophe, L.; Elster, Ch.
- Physical Review C, Vol. 98, Issue 5
Momentum space integral equations for three charged particles: Nondiagonal kernels
journal, May 2000
- Mukhamedzhanov, A. M.; Alt, E. O.; Avakov, G. V.
- Physical Review C, Vol. 61, Issue 6
Coupled-channel R-matrix method on a Lagrange mesh
journal, September 1998
- Hesse, M.; Sparenberg, J. -M.; Van Raemdonck, F.
- Nuclear Physics A, Vol. 640, Issue 1
Spin observables in three-body direct nuclear reactions
journal, April 2009
- Deltuva, A.
- Nuclear Physics A, Vol. 821, Issue 1-4
Separable representation of proton-nucleus optical potentials
journal, December 2014
- Hlophe, L.; Eremenko, V.; Elster, Ch.
- Physical Review C, Vol. 90, Issue 6
Testing the continuum-discretized coupled channels method for deuteron-induced reactions
journal, May 2012
- Upadhyay, N. J.; Deltuva, A.; Nunes, F. M.
- Physical Review C, Vol. 85, Issue 5
An approximate three-body theory of deuteron stripping
journal, December 1974
- Johnson, R. C.; Tandy, P. C.
- Nuclear Physics A, Vol. 235, Issue 1
Scattering and break-up of deuterons on α-particles in a realistic three-body model
journal, August 1983
- Bang, J.; Benayoun, J. -J.; Gignoux, C.
- Nuclear Physics A, Vol. 405, Issue 1
Ab initio many-body calculations of deuteron- scattering and states
journal, April 2011
- Navrátil, Petr; Quaglioni, Sofia
- Physical Review C, Vol. 83, Issue 4
Three-body model of light nuclei with microscopic nonlocal interactions
journal, November 2007
- Theeten, M.; Matsumura, H.; Orabi, M.
- Physical Review C, Vol. 76, Issue 5
Propagation of a deuteron in nuclear matter and the spin dependence of the deuteron optical potential
journal, April 1978
- Ioannides, A. A.; Johnson, R. C.
- Physical Review C, Vol. 17, Issue 4
Chapter III. Effects of Deuteron Virtual Breakup on Deuteron Elastic and Inelastic Scattering
journal, January 1986
- Yahiro, Masanobu; Iseri, Yasunori; Kameyama, Hirofumi
- Progress of Theoretical Physics Supplement, Vol. 89
Three-body direct nuclear reactions: Nonlocal optical potential
journal, February 2009
- Deltuva, A.
- Physical Review C, Vol. 79, Issue 2
Effects of an induced three-body force in the incident channel of ( ) reactions
journal, June 2019
- Dinmore, M. J.; Timofeyuk, N. K.; Al-Khalili, J. S.
- Physical Review C, Vol. 99, Issue 6
Ab initio many-body calculations of nucleon-nucleus scattering
journal, April 2009
- Quaglioni, Sofia; Navrátil, Petr
- Physical Review C, Vol. 79, Issue 4
Predictive theory for elastic scattering and recoil of protons from
journal, December 2014
- Hupin, Guillaume; Quaglioni, Sofia; Navrátil, Petr
- Physical Review C, Vol. 90, Issue 6
Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion
journal, September 2015
- Epelbaum, E.; Krebs, H.; Meißner, U. -G.
- Physical Review Letters, Vol. 115, Issue 12
Numerical Study of a Separable Approximation to a Local Potential
journal, December 1973
- Ernst, D. J.; Shakin, C. M.; Thaler, R. M.
- Physical Review C, Vol. 8, Issue 6
Separable representation of phenomenological optical potentials of Woods-Saxon type
journal, December 2013
- Hlophe, L.; Elster, Ch.; Johnson, R. C.
- Physical Review C, Vol. 88, Issue 6
Unified Description of Structure and Deuterium- Dynamics with Chiral Two- and Three-Nucleon Forces
journal, May 2015
- Hupin, Guillaume; Quaglioni, Sofia; Navrátil, Petr
- Physical Review Letters, Vol. 114, Issue 21
Contribution of Deuteron Breakup Channels to Deuteron Stripping and Elastic Scattering
journal, March 1970
- Johnson, R. C.; Soper, P. J. R.
- Physical Review C, Vol. 1, Issue 3
Dispersive-optical-model analysis of the asymmetry dependence of correlations in Ca isotopes
journal, October 2007
- Charity, R. J.; Mueller, J. M.; Sobotka, L. G.
- Physical Review C, Vol. 76, Issue 4
Ab Initio Many-Body Calculations of , , , and Scattering
journal, August 2008
- Quaglioni, Sofia; Navrátil, Petr
- Physical Review Letters, Vol. 101, Issue 9
Antisymmetrized deuteron stripping
journal, August 1982
- Johnson, R. C.; Austern, N.; Lopes, M. H.
- Physical Review C, Vol. 26, Issue 2
High-precision, charge-dependent Bonn nucleon-nucleon potential
journal, January 2001
- Machleidt, R.
- Physical Review C, Vol. 63, Issue 2
Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations
journal, June 1967
- Alt, E. O.; Grassberger, P.; Sandhas, W.
- Nuclear Physics B, Vol. 2, Issue 2
Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory
journal, October 2003
- Entem, D. R.; Machleidt, R.
- Physical Review C, Vol. 68, Issue 4
Unified ab initio approaches to nuclear structure and reactions
journal, April 2016
- Navrátil, Petr; Quaglioni, Sofia; Hupin, Guillaume
- Physica Scripta, Vol. 91, Issue 5
Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
journal, January 2015
- Entem, D. R.; Kaiser, N.; Machleidt, R.
- Physical Review C, Vol. 91, Issue 1
Coulomb force effects in low-energy α-deuteron scattering
journal, December 2006
- Deltuva, A.
- Physical Review C, Vol. 74, Issue 6
Deuteron-induced nucleon transfer reactions within an ab initio framework: First application to -shell nuclei
journal, May 2016
- Raimondi, Francesco; Hupin, Guillaume; Navrátil, Petr
- Physical Review C, Vol. 93, Issue 5
Separable Representations of Two-Body Interactions
journal, July 1973
- Ernst, D. J.; Shakin, C. M.; Thaler, R. M.
- Physical Review C, Vol. 8, Issue 1
Solving the resonating-group equation on a Lagrange mesh
journal, October 2002
- Hesse, M.; Roland, J.; Baye, D.
- Nuclear Physics A, Vol. 709, Issue 1-4
Ab initio predictions for polarized deuterium-tritium thermonuclear fusion
journal, January 2019
- Hupin, Guillaume; Quaglioni, Sofia; Navrátil, Petr
- Nature Communications, Vol. 10, Issue 1
Antisymmetrization corrections in deuteron elastic scattering and deuteron-induced transfer reactions
journal, March 1987
- Tostevin, J. A.; Lopes, M. H.; Johnson, R. C.
- Nuclear Physics A, Vol. 465, Issue 1
in a three-body model with realistic Forces: Separable versus nonseparable approach
journal, December 2017
- Hlophe, L.; Lei, Jin; Elster, Ch.
- Physical Review C, Vol. 96, Issue 6
New calculation schemes for proton-deuteron scattering including the Coulomb interaction
journal, May 2006
- Deltuva, A.; Fonseca, A. C.; Sauer, P. U.
- Physical Review C, Vol. 73, Issue 5