Astrophysical S -factors, Thermonuclear Rates, and Electron Screening Potential for the 3He(d,p)4He Big Bang Reaction via a Hierarchical Bayesian Model

de Souza, Rafael S.; Iliadis, Christian; Coc, Alain

doi:10.3847/1538-4357/aafda9

Title: Astrophysical S -factors, Thermonuclear Rates, and Electron Screening Potential for the ³He(d,p)⁴He Big Bang Reaction via a Hierarchical Bayesian Model

Journal Article · 11 February 2019 · The Astrophysical Journal (Online)

DOI: https://doi.org/10.3847/1538-4357/aafda9 · OSTI ID:1610383

^[1];

^[2]; Coc, Alain ^[3]

Univ. of North Carolina, Chapel Hill, NC (United States); DOE/OSTI
Univ. of North Carolina, Chapel Hill, NC (United States); Triangle Univ. Nuclear Lab. (TUNL), Durham, NC (United States)
Univ. Paris-Sud, Orsay (France)

Here, we developed a hierarchical Bayesian framework to estimate S-factors and thermonuclear rates for the ³He(d,p)⁴He reaction, which impacts the primordial abundances of ³He and ⁷Li. The available data are evaluated and all direct measurements are taken into account in our analysis for which we can estimate separate uncertainties for systematic and statistical effects. For the nuclear reaction model, we adopt a single-level, two-channel approximation of R-matrix theory, suitably modified to take the effects of electron screening at lower energies into account. In addition to the usual resonance parameters (resonance location and reduced widths for the incoming and outgoing reaction channel), we include the channel radii and boundary condition parameters in the fitting process. Our new analysis of the ³He(d,p)⁴He S-factor data results in improved estimates for the thermonuclear rates. This work represents the first nuclear rate evaluation using R-matrix theory embedded into a hierarchical Bayesian framework, properly accounting for all known sources of uncertainty. Therefore, it provides a test bed for future studies of more complex reactions.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Duke Univ., Durham, NC (United States); Univ. of North Carolina, Chapel Hill, NC (United States)

Sponsoring Organization:: National Aeronautic and Space Administration (NASA); National Aeronautics and Space Administration (NASA); USDOE Office of Science (SC); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-97ER41033; FG02-97ER41041

OSTI ID:: 1610383

Journal Information:: The Astrophysical Journal (Online), Journal Name: The Astrophysical Journal (Online) Journal Issue: 1 Vol. 872; ISSN 1538-4357

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

References (74)

Electron screening in thed+3He fusion reaction Prati, P.; Arpesella, C.; Bartolucci, F. Zeitschrift f�r Physik A Hadrons and Nuclei, Vol. 350, Issue 2 https://doi.org/10.1007/BF01290685	journal	June 1994
Differential Evolution Markov Chain with snooker updater and fewer chains ter Braak, Cajo J. F.; Vrugt, Jasper A. Statistics and Computing, Vol. 18, Issue 4 https://doi.org/10.1007/s11222-008-9104-9	journal	October 2008
A note on the 3He + D nuclear-reaction cross section Möller, W.; Besenbacher, F. Nuclear Instruments and Methods, Vol. 168, Issue 1-3 https://doi.org/10.1016/0029-554X(80)91239-2	journal	January 1980
Effects of electron screening on the 3He(d, p)4He low-energy cross sections Engstler, S.; Krauss, A.; Neldner, K. Physics Letters B, Vol. 202, Issue 2 https://doi.org/10.1016/0370-2693(88)90003-2	journal	March 1988
The single-particle limit for partial widths Dover, Carl B.; Mahaux, C.; Weidenmüller, Hans A. Nuclear Physics A, Vol. 139, Issue 3 https://doi.org/10.1016/0375-9474(69)90281-4	journal	December 1969
Low-energy fusion cross sections of D + D and D + 3He reactions Krauss, A.; Becker, H. W.; Trautvetter, H. P. Nuclear Physics A, Vol. 465, Issue 1 https://doi.org/10.1016/0375-9474(87)90302-2	journal	March 1987
Stopping power, electron screening and the astrophysical S(E) factor of d(3He,p)4He Costantini, H.; Formicola, A.; Junker, M. Physics Letters B, Vol. 482, Issue 1-3 https://doi.org/10.1016/S0370-2693(00)00513-X	journal	June 2000
Electron screening effect in the reactions 3He(d,p)4He and d(3He,p)4He Aliotta, M.; Raiola, F.; Gyürky, G. Nuclear Physics A, Vol. 690, Issue 4 https://doi.org/10.1016/S0375-9474(01)00366-9	journal	July 2001
Energy levels of light nuclei A=5, 6, 7 Tilley, D. R.; Cheves, C. M.; Godwin, J. L. Nuclear Physics A, Vol. 708, Issue 1-2 https://doi.org/10.1016/S0375-9474(02)00597-3	journal	September 2002
Electron screening in reactions between light nuclei Barker, F. C. Nuclear Physics A, Vol. 707, Issue 1-2 https://doi.org/10.1016/S0375-9474(02)00921-1	journal	August 2002
n + p → d + γ in effective field theory Savage, Martin J.; Scaldeferri, Kevin A.; Wise, Mark B. Nuclear Physics A, Vol. 652, Issue 3 https://doi.org/10.1016/S0375-9474(99)00146-3	journal	June 1999
A Note on the ³He + D Nuclear-Reaction Cross Section Möller, W.; Besenbacher, F. Ion Beam Analysis, p. 111-114 https://doi.org/10.1016/b978-1-4832-2889-1.50020-7	book	December 1979
Compilation and R-matrix analysis of Big Bang nuclear reaction rates Descouvemont, Pierre; Adahchour, Abderrahim; Angulo, Carmen Atomic Data and Nuclear Data Tables, Vol. 88, Issue 1 https://doi.org/10.1016/j.adt.2004.08.001	journal	September 2004
Probability Theory Jaynes, E. T. https://doi.org/10.1017/CBO9780511790423	book	January 2003
Data Analysis Using Regression and Multilevel/Hierarchical Models Gelman, Andrew; Hill, Jennifer https://doi.org/10.1017/CBO9780511790942	book	January 2006
Bayesian Models for Astrophysical Data Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O. Cambridge University Press https://doi.org/10.1017/CBO9781316459515	book	January 2017
The Evolution of the Universe Gamow, G. Nature, Vol. 162, Issue 4122 https://doi.org/10.1038/162680a0	journal	October 1948
The cosmological density of baryons from observations of 3He+ in the Milky Way Bania, T. M.; Rood, Robert T.; Balser, Dana S. Nature, Vol. 415, Issue 6867 https://doi.org/10.1038/415054a	journal	January 2002
Measuring the impact of COVID-19 vaccine misinformation on vaccination intent in the UK and USA Loomba, Sahil; de Figueiredo, Alexandre; Piatek, Simon J. Nature Human Behaviour, Vol. 5, Issue 3 https://doi.org/10.1038/s41562-021-01056-1	journal	February 2021
The metal-poor end of the Spite plateau: I. Stellar parameters, metallicities, and lithium abundances****** Sbordone, L.; Bonifacio, P.; Caffau, E. Astronomy & Astrophysics, Vol. 522 https://doi.org/10.1051/0004-6361/200913282	journal	October 2010
Planck 2015 results : VI. LFI mapmaking Ade, P. A. R.; Aghanim, N.; Ashdown, M. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201525813	journal	September 2016
Planck 2015 results : XIII. Cosmological parameters Ade, P. A. R.; Aghanim, N.; Arnaud, M. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201525830	journal	September 2016
Planck 2015 results : XVI. Isotropy and statistics of the CMB Ade, P. A. R.; Aghanim, N.; Akrami, Y. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201526681	journal	September 2016
Planck 2015 results : XXVI. The Second Ade, P. A. R.; Aghanim, N.; Argüeso, F. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201526914	journal	September 2016
Planck 2015 results : I. Overview of products and scientific results Adam, R.; Ade, P. A. R.; Aghanim, N. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201527101	journal	September 2016
Planck 2015 results : XXIII. The thermal Sunyaev-Zeldovich effect-cosmic infrared background correlation Ade, P. A. R.; Aghanim, N.; Arnaud, M. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201527418	journal	September 2016
Experimental Investigation and R-matrix Analysis of Low-lying Levels in 5He and 5Li Woods, Cl; Barker, Fc; Catford, Wn Australian Journal of Physics, Vol. 41, Issue 4 https://doi.org/10.1071/PH880525	journal	January 1988
Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant Riess, Adam G.; Filippenko, Alexei V.; Challis, Peter The Astronomical Journal, Vol. 116, Issue 3 https://doi.org/10.1086/300499	journal	September 1998
Three‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Implications for Cosmology Spergel, D. N.; Bean, R.; Dore, O. The Astrophysical Journal Supplement Series, Vol. 170, Issue 2 https://doi.org/10.1086/513700	journal	June 2007
The R -matrix theory Descouvemont, P.; Baye, D. Reports on Progress in Physics, Vol. 73, Issue 3 https://doi.org/10.1088/0034-4885/73/3/036301	journal	February 2010
The effects of He I λ10830 on helium abundance determinations Aver, Erik; Olive, Keith A.; Skillman, Evan D. Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 07 https://doi.org/10.1088/1475-7516/2015/07/011	journal	July 2015
Big-Bang nucleosynthesis with updated nuclear data Coc, Alain; Vangioni, Elisabeth Journal of Physics: Conference Series, Vol. 202 https://doi.org/10.1088/1742-6596/202/1/012001	journal	January 2010
Big bang Nucleosynthesis and the Helium Isotope Ratio Cooke, Ryan J. The Astrophysical Journal, Vol. 812, Issue 1 https://doi.org/10.1088/2041-8205/812/1/L12	journal	October 2015
The overlooked potential of generalized linear models in astronomy – III. Bayesian negative binomial regression and globular cluster populations de Souza, R. S.; Hilbe, J. M.; Buelens, B. Monthly Notices of the Royal Astronomical Society, Vol. 453, Issue 2 https://doi.org/10.1093/mnras/stv1825	journal	August 2015
Is the cluster environment quenching the Seyfert activity in elliptical and spiral galaxies? de Souza, R. S.; Dantas, M. L. L.; Krone-Martins, A. Monthly Notices of the Royal Astronomical Society, Vol. 461, Issue 2 https://doi.org/10.1093/mnras/stw1459	journal	June 2016
Spatial field reconstruction with INLA: application to IFU galaxy data González-Gaitán, S.; de Souza, R. S.; Krone-Martins, A. Monthly Notices of the Royal Astronomical Society, Vol. 482, Issue 3 https://doi.org/10.1093/mnras/sty2881	journal	October 2018
Higher Angular Momenta and Long Range Interaction in Resonance Reactions Wigner, E. P.; Eisenbud, L. Physical Review, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRev.72.29	journal	July 1947
On the Determination of Reduced Widths from the One-Level Dispersion Formula Thomas, R. G. Physical Review, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRev.81.148	journal	January 1951
Cross Section and Angular Distribution of the He 3 ( d , p ) He 4 Nuclear Reaction Bonner, T. W.; Conner, J. P.; Lillie, A. B. Physical Review, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRev.88.473	journal	November 1952
Angular Distribution of the Reaction He 3 ( d , p ) He 4 between 240 kev and 3.56 Mev Yarnell, J. L.; Lovberg, R. H.; Stratton, W. R. Physical Review, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRev.90.292	journal	April 1953
Cross Sections for the Reactions D ( d , p ) T , D ( d , n ) He 3 , T ( d , n ) He 4 , and He 3 ( d , p ) He 4 below 120 kev Arnold, W. R.; Phillips, J. A.; Sawyer, G. A. Physical Review, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRev.93.483	journal	February 1954
Interaction between D 2 and He 3 in the Neighborhood of the 18.6-Mev Level of Li 5 Freier, G.; Holmgren, H. Physical Review, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRev.93.825	journal	February 1954
Deuterium He 3 Reaction Kunz, W. E. Physical Review, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRev.97.456	journal	January 1955
3 2 + levels of 5 He and 5 Li, and shadow poles Barker, F. C. Physical Review C, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevC.56.2646	journal	November 1997
The 3 He ( d → , p ) 4 He reaction at low energies Geist, W. H.; Brune, C. R.; Karwowski, H. J. Physical Review C, Vol. 60, Issue 5 https://doi.org/10.1103/PhysRevC.60.054003	journal	October 1999
Bare-nucleus astrophysical factor of the He 3 ( d , p ) He 4 reaction via the “Trojan horse” method Cognata, M. La; Spitaleri, C.; Tumino, A. Physical Review C, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevC.72.065802	journal	December 2005
Radiative neutron capture on a proton at big-bang nucleosynthesis energies Ando, S.; Cyburt, R. H.; Hong, S. W. Physical Review C, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevC.74.025809	journal	August 2006
Electron screening in the He 3 ( d , p ) He 4 reaction Barker, F. C. Physical Review C, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevC.75.027601	journal	February 2007
Effective field theory as a limit of R -matrix theory for light nuclear reactions Hale, Gerald M.; Brown, Lowell S.; Paris, Mark W. Physical Review C, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevC.89.014623	journal	January 2014
Variation of fundamental constants and the role of A = 5 and A = 8 nuclei on primordial nucleosynthesis Coc, Alain; Descouvemont, Pierre; Olive, Keith A. Physical Review D, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevD.86.043529	journal	August 2012
New reaction rates for improved primordial D / H calculation and the cosmic evolution of deuterium Coc, Alain; Petitjean, Patrick; Uzan, Jean-Philippe Physical Review D, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevD.92.123526	journal	December 2015
Measurement of the Plasma Astrophysical S Factor for the He 3 ( d , p ) He 4 Reaction in Exploding Molecular Clusters Barbui, M.; Bang, W.; Bonasera, A. Physical Review Letters, Vol. 111, Issue 8 https://doi.org/10.1103/PhysRevLett.111.082502	journal	August 2013
R-Matrix Theory of Nuclear Reactions Lane, A. M.; Thomas, R. G. Reviews of Modern Physics, Vol. 30, Issue 2 https://doi.org/10.1103/RevModPhys.30.257	journal	April 1958
The cosmological constant and dark energy Peebles, P. J. E.; Ratra, Bharat Reviews of Modern Physics, Vol. 75, Issue 2 https://doi.org/10.1103/RevModPhys.75.559	journal	April 2003
Big bang nucleosynthesis: Present status Cyburt, Richard H.; Fields, Brian D.; Olive, Keith A. Reviews of Modern Physics, Vol. 88, Issue 1 https://doi.org/10.1103/RevModPhys.88.015004	journal	February 2016
The C 12 ( α , γ ) O 16 reaction and its implications for stellar helium burning deBoer, R. J.; Görres, J.; Wiescher, M. Reviews of Modern Physics, Vol. 89, Issue 3 https://doi.org/10.1103/RevModPhys.89.035007	journal	September 2017
The Evolution of the Universe Garcia-Bellido, Juan Proceedings of the International Colloquium on the Science of Time, Time and Matter https://doi.org/10.1142/9789812774392_0017	conference	January 2012
Systematic Errors Heinrich, Joel; Lyons, Louis Annual Review of Nuclear and Particle Science, Vol. 57, Issue 1 https://doi.org/10.1146/annurev.nucl.57.090506.123052	journal	November 2007
Inference from Iterative Simulation Using Multiple Sequences Gelman, Andrew; Rubin, Donald B. Statistical Science, Vol. 7, Issue 4 https://doi.org/10.1214/ss/1177011136	journal	November 1992
The Evolution of the Universe Lewis, Richard Unpublished https://doi.org/10.13140/rg.2.2.18714.98242	text	January 2021
Bayesian Estimation of Thermonuclear Reaction Rates The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/0775-4w42	text	January 2016
Bayesian Estimation of Thermonuclear Reaction Rates for Deuterium+Deuterium Reactions Iñesta,, Gómez The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/3094-4637	text	January 2017
pygtc: beautiful parameter covariance plots (aka. Giant Triangle Confusograms) Bocquet, Sebastian; W. Carter, Faustin The Journal of Open Source Software, Vol. 1, Issue 6 https://doi.org/10.21105/joss.00046	journal	October 2016
Probability Theory. By Henry E. KyburgJB . Pp. x, 294. 1969. (Prentice-Hall.) Lindley, D. V. The Mathematical Gazette, Vol. 54, Issue 389 https://doi.org/10.2307/3613841	journal	October 1970
The Evolution of the Universe Barrow, John D. New Literary History, Vol. 22, Issue 4 https://doi.org/10.2307/469068	journal	October 1991
Bayesian Estimation of Thermonuclear Reaction Rates Iliadis, C.; Anderson, K. S.; Coc, A. The Astrophysical Journal, Vol. 831, Issue 1 https://doi.org/10.3847/0004-637X/831/1/107	journal	October 2016
Bayesian Estimation of Thermonuclear Reaction Rates for Deuterium+Deuterium Reactions Gómez Iñesta, Á.; Iliadis, C.; Coc, A. The Astrophysical Journal, Vol. 849, Issue 2 https://doi.org/10.3847/1538-4357/aa9025	journal	November 2017
One Percent Determination of the Primordial Deuterium Abundance Cooke, Ryan J.; Pettini, Max; Steidel, Charles C. The Astrophysical Journal, Vol. 855, Issue 2 https://doi.org/10.3847/1538-4357/aaab53	journal	March 2018
Effective field theory as a limit of R-matrix theory for light nuclear reactions Hale, Gerald M.; Brown, Lowell S.; Paris, Mark W. arXiv https://doi.org/10.48550/arxiv.1308.0348	text	January 2013
Planck 2015 results. I. Overview of products and scientific results Collaboration, Planck; Adam, R.; Ade, P. A. R. arXiv https://doi.org/10.48550/arxiv.1502.01582	text	January 2015
The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations de Souza, R. S.; Hilbe, J. M.; Buelens, B. arXiv https://doi.org/10.48550/arxiv.1506.04792	text	January 2015
Is the cluster environment quenching the Seyfert activity in elliptical and spiral galaxies? de Souza, R. S.; Dantas, M. L. L.; Krone-Martins, A. arXiv https://doi.org/10.48550/arxiv.1603.06256	text	January 2016
Bayesian Estimation of Thermonuclear Reaction Rates Iliadis, Christian; Anderson, Kevin; Coc, Alain arXiv https://doi.org/10.48550/arxiv.1608.05853	text	January 2016
One percent determination of the primordial deuterium abundance Cooke, Ryan; Pettini, Max; Steidel, Charles C. arXiv https://doi.org/10.48550/arxiv.1710.11129	text	January 2017

Cited By (3)

Big-Bang Nucleosynthesis after Planck Fields, Brian D.; Olive, Keith A.; Yeh, Tsung-Han Journal of Cosmology and Astroparticle Physics, Vol. 2020, Issue 03 https://doi.org/10.1088/1475-7516/2020/03/010	journal	March 2020
Stress testing the dark energy equation of state imprint on supernova data Moews, Ben; de Souza, Rafael S.; Ishida, Emille E. O. Physical Review D, Vol. 99, Issue 12 https://doi.org/10.1103/physrevd.99.123529	journal	June 2019
Big-Bang Nucleosynthesis After Planck Fields, Brian D.; Olive, Keith A.; Yeh, Tsung-Han arXiv https://doi.org/10.48550/arxiv.1912.01132	text	January 2019

Similar Records

Hierarchical Bayesian Thermonuclear Rate for the ⁷Be(n,p)⁷Li Big Bang Nucleosynthesis Reaction

Journal Article · 2020 · The Astrophysical Journal (Online) · OSTI ID:1658830

de Souza, Rafael S.; Kiat, Tan Hong; Coc, Alain; +1 more

Thermonuclear fusion rates for tritium + deuterium using Bayesian methods

Journal Article · 2019 · Physical Review C · OSTI ID:1610381

de Souza, Rafael S.; Boston, S. Reece; Coc, Alain; +1 more

Bayesian Estimation Of Thermonuclear Reaction Rates

Journal Article · 2016 · The Astrophysical Journal (Online) · OSTI ID:1537160

Iliadis, C.; Anderson, K. S.; Coc, A.; +2 more

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
79 ASTRONOMY AND ASTROPHYSICS
abundances
astronomy & astrophysics
methods: statistical
nuclear reactions
nucleosynthesis

Title: Astrophysical S -factors, Thermonuclear Rates, and Electron Screening Potential for the 3He(d,p)4He Big Bang Reaction via a Hierarchical Bayesian Model

Citation Formats

References (74)

Cited By (3)

Similar Records

Related Subjects

Title: Astrophysical S -factors, Thermonuclear Rates, and Electron Screening Potential for the ³He(d,p)⁴He Big Bang Reaction via a Hierarchical Bayesian Model