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Solar fusion cross sections II: the pp chain and CNO cycles

E. G. Adelberger, A. B. Balantekin, D. Bemmerer, C. A. Bertulani, J. -W. Chen, H. Costantini, M. Couder, R. Cyburt, B. Davids, S. J. Freedman, M. Gai, A. Garcia, D. Gazit, L. Gialanella, U. Greife, M. Hass, K. Heeger, W. C. Haxton, G. Imbriani, T. Itahashi, A. Junghans, K. Kubodera, K. Langanke, D. Leitner, M. Leitner, L. E. Marcucci, T. Motobayashi, A. Mukhamedzhanov, Kenneth M. Nollett, F. M. Nunes, T. -S. Park, P. D. Parker, P. Prati, M. J. Ramsey-Musolf, R. G. Hamish Robertson, R. Schiavilla, E. C. Simpson, K. A. Snover, C. Spitaleri, F. Strieder, K. Suemmerer, H. -P. Trautvetter, R. E. Tribble, S. Typel, E. Uberseder, P. Vetter, M. Wiescher, L. Winslow

TL;DR

This Solar Fusion II review delivers updated, critically vetted cross sections and uncertainties for the pp chain and CNO cycles, integrating advances from LUNA experiments, ab initio theory, and EFT approaches. It provides recommended S(0) values for key reactions (e.g., S11(0), S12(0), S33(0), S34(0), S17(0)) and quantifies derivatives and uncertainties to propagate through standard solar model predictions, including the 8B neutrino spectrum. The work emphasizes a synthesis of model-based and ab initio methods, validated by indirect techniques such as ANC, Coulomb dissociation, and the Trojan Horse method, and proposes a coherent strategy for uncertainty treatment via inflation factors. It also outlines future facilities and techniques (e.g., underground accelerators and recoil separators) to push measurements closer to solar Gamow peaks, thereby sharpening tests of solar physics, neutrino properties, and stellar evolution. Overall, Solar Fusion II strengthens the nuclear input to the solar model, enables more precise neutrino flux predictions, and guides experimental and theoretical efforts toward reducing remaining uncertainties in stellar nuclear processes.

Abstract

We summarize and critically evaluate the available data on nuclear fusion cross sections important to energy generation in the Sun and other hydrogen-burning stars and to solar neutrino production. Recommended values and uncertainties are provided for key cross sections, and a recommended spectrum is given for 8B solar neutrinos. We also discuss opportunities for further increasing the precision of key rates, including new facilities, new experimental techniques, and improvements in theory. This review, which summarizes the conclusions of a workshop held at the Institute for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to Reviews of Modern Physics 70 (1998) 1265.

Solar fusion cross sections II: the pp chain and CNO cycles

TL;DR

This Solar Fusion II review delivers updated, critically vetted cross sections and uncertainties for the pp chain and CNO cycles, integrating advances from LUNA experiments, ab initio theory, and EFT approaches. It provides recommended S(0) values for key reactions (e.g., S11(0), S12(0), S33(0), S34(0), S17(0)) and quantifies derivatives and uncertainties to propagate through standard solar model predictions, including the 8B neutrino spectrum. The work emphasizes a synthesis of model-based and ab initio methods, validated by indirect techniques such as ANC, Coulomb dissociation, and the Trojan Horse method, and proposes a coherent strategy for uncertainty treatment via inflation factors. It also outlines future facilities and techniques (e.g., underground accelerators and recoil separators) to push measurements closer to solar Gamow peaks, thereby sharpening tests of solar physics, neutrino properties, and stellar evolution. Overall, Solar Fusion II strengthens the nuclear input to the solar model, enables more precise neutrino flux predictions, and guides experimental and theoretical efforts toward reducing remaining uncertainties in stellar nuclear processes.

Abstract

We summarize and critically evaluate the available data on nuclear fusion cross sections important to energy generation in the Sun and other hydrogen-burning stars and to solar neutrino production. Recommended values and uncertainties are provided for key cross sections, and a recommended spectrum is given for 8B solar neutrinos. We also discuss opportunities for further increasing the precision of key rates, including new facilities, new experimental techniques, and improvements in theory. This review, which summarizes the conclusions of a workshop held at the Institute for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to Reviews of Modern Physics 70 (1998) 1265.

Paper Structure

This paper contains 73 sections, 57 equations, 20 figures, 13 tables.

Table of Contents

  1. INTRODUCTION
  2. Solar Fusion II: the 2009/10 effort
  3. Contents of this review
  4. NUCLEAR REACTIONS IN HYDROGEN-BURNING STARS
  5. Rates and S-factors
  6. Screening of stellar and laboratory reactions
  7. Fitting and extrapolating S-factors
  8. Theory constraints: model-based methods
  9. Theory constraints: ab initio methods
  10. Adopted procedures
  11. Treatment of uncertainties
  12. THE pp REACTION
  13. Progress in potential models
  14. Progress in effective field theory (EFT)
  15. Hybrid EFT (EFT*)
  16. ...and 58 more sections

Figures (20)

  • Figure 1: The stellar energy production as a function of temperature for the pp chain and CN cycle, showing the dominance of the former at solar temperatures. Solar metallicity has been assumed. The dot denotes conditions in the solar core: the Sun is powered dominantly by the pp chain.
  • Figure 2: The left frame shows the three principal cycles comprising the pp chain (ppI, ppII, and ppIII), with branching percentages indicated, each of which is "tagged" by a distinctive neutrino. Also shown is the minor branch ${}^3$He+p $\rightarrow$${}^4$He+e$^+$+$\nu_e$, which burns only $\sim$ 10$^{-7}$ of ${}^3$He, but produces the most energetic neutrinos. The right frame shows the CNO bi-cycle. The CN cycle, marked I, produces about 1% of solar energy and significant fluxes of solar neutrinos.
  • Figure 3: (Color online) The astrophysical S$_{12}$-factor datasets Gri62Sch96ma97luna are plotted together with theoretical predictions of Marcucci05. The solid line represents the "full" theoretical calculation, while the red band represents the 68% lower and upper bounds of the adopted quadratic best fit to the four experimental datasets (see text and Eq. (\ref{['eq:s12quad']}) for more explanation). In the insert, the S$_{12}$-factor of the $^2$H(p,$\gamma$)$^3$He reaction in the energy range 0-50 keV, obtained with the Argonne $v_{18}$ two-nucleon and Urbana IX three-nucleon Hamiltonian model in the impulse approximation (dashed line) and with inclusion of interaction currents (solid line), is compared with the experimental results.
  • Figure 4: (Color online) The data, the best quadratic+screening result for S$_{33}(E)$, and the deduced best quadratic fit (red line) and allowed range (yellow band) for S$^\mathrm{bare}_{33}$. See text for references.
  • Figure 5: (Color online) S$_{34}(E)$ vs. $E$. Data points: LUNA - green circles; Weizmann - red squares; UW-Seattle - blue diamonds; ERNA - brown triangles. Solid curve - best fit scaled Nollett theory to the data with $E$$\leq$ 1.002 MeV. The yellow band indicates the $\pm$1-$\sigma$ error band. Data are shown with statistical-plus-varying-systematic errors only; overall systematic errors are not included.
  • ...and 15 more figures