In stars that lie on the main sequence in the Hertzsprung-Russel diagram, like our sun, hydrogen is fused to helium in a number of nuclear reaction chains and series, such as the proton-proton chain and the carbon-nitrogen-oxygen cycles. Precisely determined thermonuclear rates of these reactions lie at the foundation of the standard solar model. This review, the third decadal evaluation of the nuclear physics of hydrogen-burning stars, is motivated by the great advances made in recent years by solar neutrino observatories, putting experimental knowledge of the proton-proton chain neutrino fluxes in the few-percent precision range. The basis of the review is a one-week community meeting held in July 2022 in Berkeley, California, and many subsequent digital meetings and exchanges. The relevant reactions of solar and stellar hydrogen burning are reviewed here, from both theoretical and experimental perspectives. Recommendations for the state of the art of the astrophysical S-factor and its uncertainty are formulated for each of them. Several other topics of paramount importance for the solar model are reviewed, as well: recent and future neutrino experiments, electron screening, radiative opacities, and current and upcoming experimental facilities. In addition to reaction-specific recommendations, also general recommendations are formed.

The N-15(alpha,gamma)F-19 reaction produces F-19 in asymptotic giant branch (AGB) stars, where the low energy tails of two resonances at E-c.m.=1323 +/- 2 and 1487 +/- 1.7 keV are estimated to contribute about 30% of the total reaction rate in these environments. However, recent measurements have shown discrepancies in the energies, the strengths, and the corresponding alpha widths of these two resonances, resulting in an increase in the systematic uncertainty of the extrapolated cross section to helium burning energies. With this motivation, we have undertaken new measurements of the N-15(alpha,gamma)F-19 at the University of Notre Dame Nuclear Science Laboratory. The setup consisted of an alpha particle beam impinged on a solid (TiN)-N-15 target with gamma-ray spectroscopy accomplished using a high purity germanium detector. Using the Doppler corrected gamma-ray energies, we confirmed the lower resonance energy to be 1321.6 +/- 0.6 keV and found a value for the higher one of 1479.4 +/- 0.6 keV that is more consistent with those found from previous elastic scattering studies. We found that the resonance strengths for both were consistent with most values found in the literature, but a larger alpha width has been recommended for the E-c.m.=1487 keV resonance. The larger alpha width suggests a reaction rate increase of about 15% at temperatures T<0.1 GK relevant to low mass AGB stars. The impact of the increased reaction rate requires further investigations.

The ^24 Mg( α ,p) ^27 Al reaction was measured using the solenoid spectrometer for nuclear astrophysics at the University of the Notre Dame to study the astrophysical ^24 Mg( α ,p) ^27 Al reaction rate. Alpha beams from the 10-MV FN tandem accelerator impinged on ^24 Mg solid targets which were made using the vacuum evaporation method on ^12 C foils. A total of 43 beam energies were used. Recoiling protons from the ^24 Mg( α ,p) ^27 Al reaction were detected using a double-sided position sensitive silicon detector array mounted on the solenoid. Energies, times of flight, and flight distances of particles were measured for particle identification. Protons associated with a wide range of excitation energies E_x = 12.42–14.44 MeV in ^28 Si were identified.

The Istituto Nazionale di Fisica Nucleare—Laboratori Nazionali del Gran Sasso (LNGS) is one of the largest underground physics laboratory, a very peculiar environment suited for experiments in Astroparticle Physics, Nuclear Physics and Fundamental Symmetries. The newly established Bellotti Ion Beam facility represents a major advance in the possibilities of studying nuclear processes in an underground environment. A workshop was organized at LNGS in the framework of the Nuclear Physics Mid Term Plan in Italy, an initiative of the Nuclear Physics Division of the Instituto Nazionale di Fisica Nucleare to discuss the opportunities that will be possible to study in the near future by employing state-of-the-art detection systems. In this report, a detailed discussion of the outcome of the workshop is presented.

The $^{15}\mathrm{N}$($\ensuremath{\alpha},\ensuremath{\gamma}$)$^{19}\mathrm{F}$ reaction produces $^{19}\mathrm{F}$ in asymptotic giant branch (AGB) stars, where the low energy tails of two resonances at ${E}_{\mathrm{c}.\mathrm{m}.}=1323\ifmmode\pm\else\textpm\fi{}2$ and $1487\ifmmode\pm\else\textpm\fi{}1.7\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ are estimated to contribute about 30% of the total reaction rate in these environments. However, recent measurements have shown discrepancies in the energies, the strengths, and the corresponding alpha widths of these two resonances, resulting in an increase in the systematic uncertainty of the extrapolated cross section to helium burning energies. With this motivation, we have undertaken new measurements of the $^{15}\mathrm{N}$($\ensuremath{\alpha},\ensuremath{\gamma}$)$^{19}\mathrm{F}$ at the University of Notre Dame Nuclear Science Laboratory. The setup consisted of an alpha particle beam impinged on a solid $\mathrm{Ti}^{15}\mathrm{N}$ target with gamma-ray spectroscopy accomplished using a high purity germanium detector. Using the Doppler corrected gamma-ray energies, we confirmed the lower resonance energy to be $1321.6\ifmmode\pm\else\textpm\fi{}0.6\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ and found a value for the higher one of $1479.4\ifmmode\pm\else\textpm\fi{}0.6\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ that is more consistent with those found from previous elastic scattering studies. We found that the resonance strengths for both were consistent with most values found in the literature, but a larger alpha width has been recommended for the ${E}_{\mathrm{c}.\mathrm{m}.}=1487\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ resonance. The larger alpha width suggests a reaction rate increase of about $15%$ at temperatures $T<0.1$ GK relevant to low mass AGB stars. The impact of the increased reaction rate requires further investigations.

The cross section of the C13(α,n)O16 reaction is needed for nuclear astrophysics and applications to a precision of 10% or better, yet inconsistencies among 50 years of experimental studies currently lead to an uncertainty of ≈15%. Using a state-of-the-art neutron detection array, we have performed a high resolution differential cross section study covering a broad energy range. These measurements result in a dramatic improvement in the extrapolation of the cross section to stellar energies potentially reducing the uncertainty to ≈5% and resolving long standing discrepancies in higher energy data.Received 18 March 2023Revised 5 September 2023Accepted 17 January 2024DOI:https://doi.org/10.1103/PhysRevLett.132.062702© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasH & He burningH & He induced nuclear reactionsHydrostatic stellar nucleosynthesisNeutron physicsResonance reactionsS-factors processProperties6 ≤ A ≤ 19TechniquesNuclear data analysis & compilationNuclear Physics

Since He et al. [J. J. He et al., Phys. Lett. B 725, 287 (2013)] postulated the existence of a new, low-lying, broad resonance in the 6Li(p, gamma ) 7Be reaction, there have been several studies that have looked to further investigate this assertion. However, none of these approaches has utilized the stringent constraint imposed by the unitarity of the scattering matrix. That is, the corresponding compound nucleus state must produce a corresponding resonance in 3He(alpha, alpha) 3He and 6Li(p, p) 7Li scattering and the 6Li(p, alpha) 3He reaction. Since precision data are readily available in the literature, the level of consistency can be tested using a phenomenological R-matrix analysis. In addition, remaining discrepancies with the description of the 6Li(p, gamma ) 7Be reaction are discussed.

The cross section of the ^{13}C(α,n)^{16}O reaction is needed for nuclear astrophysics and applications to a precision of 10% or better, yet inconsistencies among 50 years of experimental studies currently lead to an uncertainty of ≈15%. Using a state-of-the-art neutron detection array, we have performed a high resolution differential cross section study covering a broad energy range. These measurements result in a dramatic improvement in the extrapolation of the cross section to stellar energies potentially reducing the uncertainty to ≈5% and resolving long standing discrepancies in higher energy data.

Indirect methods have proven to be a complementary approach for extending our knowledge of nuclear structure and low-energy cross sections. Among these, the neutron-induced reaction cross sections appear to be of particular interest since their role both for unstable and stable beams. In view of this, we report here the combined study of the 17O(n, alpha)14C reaction accomplished by the Trojan Horse Method (THM) and the asymptotic normalization coefficient (ANC) method. The low-lying 8038, 8125, 8213, and 8282 keV resonances in 18O are studied, and their Gamma n are derived. A comparison with recent direct data and recent THM experimental data is presented. The independent ANC investigation corroborates our previous THM results, confirms the consistence of the two indirect investigations, and shows new frontiers for neutron-induced reactions with radioactive ion beams. Moreover, we examined the impact of adopting the newly recommended 17O(n, alpha)14C reaction rate on asymptotic giant branch stars' nucleosynthesis. Our findings reveal significant variations (greater than or similar to 10%) in the production of the neutron-rich heavy isotopes sensitive to neutron density, underlining the neutron-poisoning effect of 17O on the s-process.

The interplay between the 22Ne(alpha, gamma ) 26Mg reaction and the competing 22Ne(alpha, n) 25Mg reaction determines the efficiency of the latter as a neutron source at the temperatures of stellar helium burning. In both cases, the rates are dominated by the alpha-cluster resonance at 830 keV. This resonance plays a particularly important role in determining the strength of the neutron flux for both the weak and main s process as well as the n process. Recent experimental studies based on transfer reactions suggest that the neutron and gamma -ray strengths for this resonance are approximately equal. In this study, the 22Ne(alpha, n) 25Mg resonance strength has been remeasured and found to be similar to the previous direct studies. This reinforces an 830 keV resonance strength that is approximately a factor of 3 larger for the 22Ne(alpha, n) 25Mg reaction than for the 22Ne(alpha, gamma ) 26Mg reaction.

Physics models typically contain adjustable parameters to reproduce measured data. While some parameters correspond directly to measured features in the data, others are unobservable. These unobservables can, in some cases, cause ambiguities in the extraction of observables from measured data, or lead to questions on the physical interpretation of fits that require these extra parameters. We propose a method based on deep learning to extract values of observables directly from the data without the need for unobservables. The key to our approach is to label the training data for the deep learning model with only the observables. After training, the deep learning model can determine the values of observables from measured data with no ambiguities arising from unobservables. We demonstrate this method on the phenomenological R-matrix that is widely utilized in nuclear physics to extract resonance parameters from cross section data. Our deep learning model based on Transformers successfully predicts nuclear properties from measurements with no need for the channel radius and background pole parameters required in traditional R-matrix analyses. Details and limitations of this method, which may be useful for studies of a wide range of phenomena, are discussed.

Background: The 12 C( alpha, gamma ) 16 O reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the 16O nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2+) and (7.12 MeV, 1-), that dominate the behavior of the low-energy S factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. Purpose: The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy S factor, especially at the key astrophysical energy of 300 keV. Method: The S factors are calculated within the framework of the R-matrix method using the AZURE2 code. Results: Our total S factor takes into account the E 1 and E 2 transitions to the ground state of 16O including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of 16O through four subthreshold states: 0+2 , 3-, 2+, and 1-. To evaluate the impact of subthreshold ANCs on the low-energy S factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev et al., Eur. Phys. J. A 59 , 162 (2023)]. The set with low ANC values was employed by deBoer et al. [Rev. Mod. Phys. 89 , 035007 (2017)]. A detailed comparison of the S factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this S factor. Conclusion: The contribution to the total E 1 and E 2 S factors from the corresponding subthreshold resonances at 300 keV are (71-74)% and (102-103)%, respectively. The correlation of the uncertainties of the subthreshold ANCs with the E 1 and E 2 S (300keV) factors is found. The E 1 transition of the subthreshold resonance 1- does not depend on the ground-state ANC but interferes constructively with a broad (9.585 MeV; 1-) resonance giving (for the present subthreshold ANC) an additional 26% contribution to the total E 1 S (300keV) factor. Interference of the E 2 transition through the subthreshold resonance 2+ with direct capture is almost negligible for small ground-state ANC of 58 fm-1/2. However, its interference with direct capture for higher ground-state ANC of 337 fm-1/2 is significant and destructive, contributing - 27%. The low-energy S E 2 (300keV) factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase.

Deuteron-induced reactions on 6Li are important for nuclear structure studies and nuclear applications. A new experimental effort was dedicated to improve incomplete partial cross sections and the angular distribution information for d + 6Li reactions and to address the inconsistencies between various R-matrix evaluations of the 8Be system. The new measurements were performed over a deuteron energy range of 1.8 to 10 MeV with an angular distribution coverage of 20 degrees-170 degrees for outgoing particles. The experiment simultaneously measured neutrons, charged particles, and gamma rays from the various exit channels of the d + 6Li reaction. The cross sections for open reaction channels measured simultaneously are presented. In addition, results for the 6Li(d, n) 7Be total cross section using the activation method are also presented.

The cross section of the 13C(alpha, n)16O reaction is needed for nuclear astrophysics and applications to a precision of 10% or better, yet inconsistencies among 50 years of experimental studies currently lead to an uncertainty of approximate to 15%. Using a state-of-the-art neutron detection array, we have performed a high resolution differential cross section study covering a broad energy range. These measurements result in a dramatic improvement in the extrapolation of the cross section to stellar energies potentially reducing the uncertainty to approximate to 5% and resolving long standing discrepancies in higher energy data.

Nucleosynthesis in primordial stellar environments may lead to a substantial production of 10B isotopes, which either are converted by the 10B(p, alpha) 7Be reaction to 7Be or processed further by 10B +alpha reactions towards the carbon, nitrogen, and oxygen range. This paper focuses on low energy studies of the 10B(alpha, p)13C and 10B(alpha, d)12C reactions to determine the low energy cross section and the reaction rates in stellar environments using R-matrix analysis techniques. The experimental results cover a broad energy range, from 0.21 MeV up to 1.4 MeV in the center of mass frame, extending down to the Gamow energy range. A substantial increase in the reaction rate compared to previous predictions is found, due to the identification of near threshold alpha-cluster resonance structures.

Solar neutrino measurements have recently reached a level of sensitivity such that CNO fluxes can now be experimentally determined. While these first measurements are still only sensitive to the higher energy neutrinos resulting from the & beta;+ decays of 15O produced by the 14N(p, & gamma; ) 15O reaction, future measurements will work towards detection of neutrinos from the & beta;+ decay of 13N from the 12C(p, & gamma; )13N reaction. This paper reports on a recent measurement of the 12C(p, & gamma; ) 13N reaction covering a broad laboratory energy range between 1.0 and 2.5 MeV. The measurement was made to better determine the overall normalization of the absolute cross section and to explore the interference effects between the two broad, overlapping resonances at proton energies of 0.460 and 1.689 MeV and the direct capture to the ground state of 13N in the framework of a multichannel R-matrix analysis. This work takes into account previous radiative capture as well as elastic 12C(p, p) 12C scattering data, making uncertainty estimations using a Bayesian framework, to determine a reliable extrapolation of the low energy S factor towards the stellar energy range of CNO hydrogen burning. These new experimental results, and a detailed investigation of the past literature data, suggest that the resonant component of the cross section should be 30% lower than previously accepted.

Solar neutrino measurements have recently reached a level of sensitivity such that CNO fluxes can now be experimentally determined. While these first measurements are still only sensitive to the higher energy neutrinos resulting from the ${\ensuremath{\beta}}^{+}$ decays of $^{15}\mathrm{O}$ produced by the $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$ reaction, future measurements will work towards detection of neutrinos from the ${\ensuremath{\beta}}^{+}$ decay of $^{13}\mathrm{N}$ from the $^{12}\mathrm{C}(p,\ensuremath{\gamma})^{13}\mathrm{N}$ reaction. This paper reports on a recent measurement of the $^{12}\mathrm{C}(p,\ensuremath{\gamma})^{13}\mathrm{N}$ reaction covering a broad laboratory energy range between 1.0 and 2.5 MeV. The measurement was made to better determine the overall normalization of the absolute cross section and to explore the interference effects between the two broad, overlapping resonances at proton energies of 0.460 and 1.689 MeV and the direct capture to the ground state of $^{13}\mathrm{N}$ in the framework of a multichannel $R$-matrix analysis. This work takes into account previous radiative capture as well as elastic $^{12}\mathrm{C}(p,p)^{12}\mathrm{C}$ scattering data, making uncertainty estimations using a Bayesian framework, to determine a reliable extrapolation of the low energy $S$ factor towards the stellar energy range of CNO hydrogen burning. These new experimental results, and a detailed investigation of the past literature data, suggest that the resonant component of the cross section should be 30% lower than previously accepted.

We present results from direct measurements of the total C-13(alpha, n) O-16 cross section over laboratory energies E-alpha = 2.9-8.0 MeV, performed with the (HeBF3)-He-3 giant barrel neutron detector at the Edwards Accelerator Laboratory. The cross sections reported in this work are considerably lower than prior direct measurements for E-alpha > 5 MeV, in agreement with prior corrections based on Hauser-Feshbach estimates. However, applying branching ratios based on Hauser-Feshbach estimates to our data would not reproduce existing direct measurements for partial decay channels. This indicates both the promise and limitations of Hauser-Feshbach for branching ratio estimates of (alpha, n) reactions on light nuclides. The C-13(alpha, n) thick-target yields inferred from this work for E-alpha > 6 MeV are significantly larger than those currently employed in estimates of dark matter and neutrino detector backgrounds.