ABSOLUTE CROSS SECTION FOR THE REACTION T(d,n)He$sup 4$ FROM 10 TO 120 KEV

Arnold, W.; Phillips, J. A.; Sawyer, G.A.; Stovall, E.J.; Tuck, J.L.

doi:10.2172/4374823

Cited by 3 publications

(15 citation statements)

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“…[11,12,21] the extrinsic scatter is smaller, or of similar magnitude, compared to the reported statistical uncertainties. However, our derived extrinsic scatter for the data of Arnold et al [22], σ S,extr = 0.471 +0.043 −0.038 MeVb, exceeds their reported statistical uncertainties by more than an order of magnitude (Table VIII). This indicates that the latter authors underestimated their statistical uncertainties.…”

Section: Normalization and Extrinsic Scattercontrasting

confidence: 41%

“…We evaluated the published data and adopted those experiments for which separate estimates of systematic and statistical uncertainties can be obtained: Jarmie, Brown and Hardekopf [11]; Brown, Jarmie and Hale [12]; Kobzev, Salatskij and Telezhnikov [21]; Arnold et al [22]; and Conner, Bonner and Smith [6]. The difficulties and special circumstances when studying the exceptionally broad low-energy resonance in this reaction are discussed in detail.…”

Section: Discussionmentioning

confidence: 99%

“…The data used in our analysis: (Red circles) Jarmie, Brown and Hardekopf [11]; (Black diamonds) Brown, Jarmie and Hale [12]; (Green squares) Kobzev, Salatskij and Telezhnikov [21]; (Blue triangles) Arnold et al [22]; (Purple triangles) Conner, Bonner and Smith [6]. Absolute cross sections were not determined in Ref.…”

Section: Data Selectionmentioning

confidence: 99%

“…All of our adopted data are shown in Figure 1. They originated from the experiments by Jarmie, Brown and Hardekopf [11], Brown, Jarmie and Hale [12], Kobzev, Salatskij and Telezhnikov [21], Arnold et al [22], and Conner, Bonner and Smith [6], and contain 191 data points in the center-of-mass energy region between 5 keV and 270 keV. Notice that the results of Ref.…”

Section: Data Selectionmentioning

confidence: 99%

“…The systematic S-factor uncertainties for the data of Jarmie, Brown and Hardekopf [11], Kobzev, Salatskij and Telezhnikov [21], Arnold et al [22], and Conner, Bonner and Smith [6] amount to 1.26%, 2.5%, 2.0%, and 1.8%, respectively (Appendix A). These correspond to factor uncertainties of (f.u.)…”

Section: Preliminary Considerationsmentioning

confidence: 99%

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Thermonuclear fusion rates for tritium + deuterium using Bayesian methods

et al. 2019

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The 3 H(d,n) 4 He reaction has a large low-energy cross section and will likely be utilized in future commercial fusion reactors. This reaction also takes place during big bang nucleosynthesis. Studies of both scenarios require accurate and precise fusion rates. To this end, we implement a onelevel, two-channel R-matrix approximation into a Bayesian model. Our main goals are to predict reliable astrophysical S-factors and to estimate R-matrix parameters using the Bayesian approach. All relevant parameters are sampled in our study, including the channel radii, boundary condition parameters, and data set normalization factors. In addition, we take uncertainties in both measured bombarding energies and S-factors rigorously into account. Thermonuclear rates and reactivities of the 3 H(d,n) 4 He reaction are derived by numerically integrating the Bayesian S-factor samples. The present reaction rate uncertainties at temperatures between 1.0 MK and 1.0 GK are in the range of 0.2% to 0.6%. Our reaction rates differ from previous results by 2.9% near 1.0 GK. Our reactivities are smaller than previous results, with a maximum deviation of 2.9% near a thermal energy of 4 keV. The present rate or reactivity uncertainties are more reliable compared to previous studies that did not include the channel radii, boundary condition parameters, and data set normalization factors in the fitting. Finally, we investigate previous claims of electron screening effects in the published 3 H(d,n) 4 He data. No such effects are evident and only an upper limit for the electron screening potential can be obtained.

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Section: Normalization and Extrinsic Scattercontrasting

confidence: 41%

Section: Discussionmentioning

confidence: 99%

Section: Data Selectionmentioning

confidence: 99%

Section: Data Selectionmentioning

confidence: 99%

Section: Preliminary Considerationsmentioning

confidence: 99%

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Thermonuclear fusion rates for tritium + deuterium using Bayesian methods

et al. 2019

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Nuclear Reaction d + t → α + n

Valković¹

2015

14 MeV Neutrons

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How Bayesian methods can improve $R$-matrix analyses of data: the example of the $dt$ Reaction

Odell,

Brune,

Phillips

2021

Preprint

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The 3 H(d, n) 4 He reaction is of significant interest in nuclear astrophysics and nuclear applications. It is an important, early step in big-bang nucleosynthesis and a key process in nuclear fusion reactors. We use one-and two-level R-matrix approximations to analyze data on the cross section for this reaction at center-of-mass energies below 215 keV. We critically examine the data sets using a Bayesian statistical model that allows for both common-mode and additional point-to-point uncertainties. We use Markov Chain Monte Carlo sampling to evaluate this R-matrix-plus-statistical model and find two-level R-matrix results that are stable with respect to variations in the channel radii. The S factor at 40 keV evaluates to 25.36(19) MeV b (68% credibility interval). We discuss our Bayesian analysis in detail and provide guidance for future applications of Bayesian methods to R-matrix analyses. We also discuss possible paths to further reduction of the S-factor uncertainty.

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ABSOLUTE CROSS SECTION FOR THE REACTION T(d,n)He$sup 4$ FROM 10 TO 120 KEV

Cited by 3 publications

References 0 publications

Thermonuclear fusion rates for tritium + deuterium using Bayesian methods

Thermonuclear fusion rates for tritium + deuterium using Bayesian methods

Nuclear Reaction d + t → α + n

How Bayesian methods can improve $R$-matrix analyses of data: the example of the $dt$ Reaction

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