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Compilation and R-matrix analysis of Big Bang nuclear reaction rates

Pierre Descouvemont, Abderrahim Adahchour, Carmen Angulo, Alain Coc, Elisabeth Vangioni-Flam

TL;DR

This work addresses the critical need for precise nuclear reaction rates in Standard Big-Bang Nucleosynthesis by applying the $R$-matrix formalism to low-energy cross sections and providing statistically rigorous uncertainty estimates. The authors parameterize reactions with a controlled set of poles, separating internal nuclear dynamics from external Coulomb behavior, and connect formal and observed resonance parameters to extract reliable rates. They quantify uncertainties using PDG96 methods, including the covariance matrix, and carefully handle data-set normalization issues to produce robust rate estimates. The resulting updated $S$-factors and reaction rates, with reduced uncertainties and detailed comparisons to NACRE and SKM, enable tighter cosmological constraints when confronting CMB-derived baryon densities from experiments like WMAP; all rates and factors are made publicly available for the community.

Abstract

We use the R-matrix theory to fit low-energy data on nuclear reactions involved in Big Bang nucleosynthesis. A special attention is paid to the rate uncertainties which are evaluated on statistical grounds. We provide S factors and reaction rates in tabular and graphical formats.

Compilation and R-matrix analysis of Big Bang nuclear reaction rates

TL;DR

This work addresses the critical need for precise nuclear reaction rates in Standard Big-Bang Nucleosynthesis by applying the -matrix formalism to low-energy cross sections and providing statistically rigorous uncertainty estimates. The authors parameterize reactions with a controlled set of poles, separating internal nuclear dynamics from external Coulomb behavior, and connect formal and observed resonance parameters to extract reliable rates. They quantify uncertainties using PDG96 methods, including the covariance matrix, and carefully handle data-set normalization issues to produce robust rate estimates. The resulting updated -factors and reaction rates, with reduced uncertainties and detailed comparisons to NACRE and SKM, enable tighter cosmological constraints when confronting CMB-derived baryon densities from experiments like WMAP; all rates and factors are made publicly available for the community.

Abstract

We use the R-matrix theory to fit low-energy data on nuclear reactions involved in Big Bang nucleosynthesis. A special attention is paid to the rate uncertainties which are evaluated on statistical grounds. We provide S factors and reaction rates in tabular and graphical formats.

Paper Structure

This paper contains 13 sections, 35 equations, 13 figures, 16 tables.

Table of Contents

  1. INTRODUCTION
  2. The $R$-matrix method
  3. General formalism
  4. Elastic scattering
  5. Transfer reactions
  6. Radiative-capture cross sections
  7. Treatment of uncertainties
  8. Calculation of Reaction rates
  9. Definition
  10. Screening effects
  11. Physical constants
  12. Cross sections and reaction rates
  13. References

Figures (13)

  • Figure 1: Illustration of case 2 (see text). Full circles and squares represent the original experimental data (units are arbitrary); open symbols are extrapolated values, and triangles represent the "effective" cross sections (\ref{['eq305']}).
  • Figure I.a: $\hbox{$^2$H(p,$\gamma$)$^3$He}$$S$ factor. The data are taken from Ref. Gr62 (Griffiths 62), Ref. Gr63 (Griffiths 63), Ref. Wa63 (Warren 63), Ref. WO67 (Wolfli 67), Ref. Ba70 (Bailey 70), Ref. Sk79 (Skopic 79), Ref. Sc97 (Schmid 97), Ref. Ma97 (Ma 97), and Ref. Lu02 (LUNA 02).
  • Figure I.b: $\hbox{$^2$H(d,n)$^3$He}$$S$ factor. The data are taken from Ref. SC72 (Schulte 72), Ref. KR87a (Krauss 87), Ref. BR90 (Brown 90), and Ref. GR95 (Greife 95). The dotted curves represent the individual fits.
  • Figure I.c: $\hbox{$^2$H(d,p)$^3$H}$$S$ factor. The data are taken from Ref. SC72 (Schulte 72), Ref. KR87a (Krauss 87), Ref. BR90 (Brown 90), and Ref. GR95 (Greife 95). The dotted curve represents the individual fit to Ref. KR87a. Individual fits of Ref. BR90 and GR95 are very close to the global fit.
  • Figure I.d: $\hbox{$^3$H(d,n)$^4$He}$$S$ factor. The data are taken from Ref. AR52 (Argo 52), Ref. CO52 (Conner 52), Ref. AR54 (Arnold 54), Ref. BA57 (Bame 57), Ref. KO66 (Kobzev 66), Ref. MC73 (McDaniels), Ref. JA84 (Jarmie 84), and Ref. BR87a (Brown 87).
  • ...and 8 more figures