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Solar Fusion Cross Sections II: the Pp Chain and CNO Cycles

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Solar Fusion Cross Sections II: the Pp Chain and CNO Cycles Solar fusion cross sections II: the pp chain and CNO cycles E. G. Adelberger, A. Garc´ıa,R. G. Hamish Robertson, and K. A. Snover Department of Physics and Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, WA 98195 USA A. B. Balantekin, K. Heeger, and M. J. Ramsey-Musolf Department of Physics, University of Wisconsin, Madison, WI 53706 USA D. Bemmerer and A. Junghans Forschungszentrum Dresden-Rossendorf, D-01314 Dresden, Germany C. A. Bertulani Department of Physics and Astronomy, Texas A&M University, Commerce, TX 75429 USA J.-W. Chen Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan H. Costantini and P. Prati Universit`adi Genova and INFN Sezione di Genova, Genova, Italy M. Couder, E. Uberseder, and M. Wiescher Department of Physics and JINA, University of Notre Dame, Notre Dame, IN 46556 USA R. Cyburt JINA and National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 USA B. Davids TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada V6T 2A3 S. J. Freedman Department of Physics, University of California, Berkeley, and Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA M.Gai Laboratory for Nuclear Sciences at Avery Point, University of Connecticut, CT 06340-6097 and Department of Physics, Yale University, New Haven, CT 06520-8124 USA D. Gazit Institute for Nuclear Theory, University of Washington, Seattle, WA 98195 USA and Racah Institute of Physics, The Hebrew University, Jerusalem, 91904, Israel L. Gialanella and G. Imbriani Dipartimento di Scienze Fisiche, Universit`adi Napoli, and INFN Sezione di Napoli, Napoli, Italy U. Greife Department of Physics, Colorado School of Mines, Golden, CO 80401 USA M. Hass Department of Particle Physics and Astrophysics, The Weizmann Institute, Rehovot, Israel W. C. Haxton Department of Physics, University of California, Berkeley, and Lawrence Berkeley National Laboratory, Berkeley, CA 94720 and Institute for Nuclear Theory, University of Washington, Seattle, WA 98195 USA T. Itahashi Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047 Japan 2 K. Kubodera Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208 USA K. Langanke GSI Helmholtzzentrum f¨urSchwerionenforschung, D-64291 Darmstadt, Germany, Institut f¨urKernphysik, Universit¨at Darmstadt, Germany and Frankfurt Institute for Advanced Studies, Frankfurt, Germany D. Leitner, M. Leitner, P. Vetter, and L. Winslow Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA L. E. Marcucci Department of Physics "E. Fermi", University of Pisa, and INFN Sezione di Pisa, Largo B. Pontecorvo 3, I-56127, Pisa, Italy T. Motobayashi The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan A. Mukhamedzhanov and R. E. Tribble Cyclotron Institute, Texas A&M University, College Station, TX 77843 USA Kenneth M. Nollett Physics Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439 USA F. M. Nunes National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 USA T.-S. Park Department of Physics and BAERI, Sungkyunkwan University, Suwon 440-746 Korea P. D. Parker Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520 USA R. Schiavilla Department of Physics, Old Dominion University, Norfolk, VA 23529 and Jefferson Laboratory, Newport News, VA 23606 USA E. C. Simpson Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom C. Spitaleri INFN Laboratori Nazionali del Sud & DMFCI, Universit`adi Catania, Catania, Italy F. Strieder and H.-P. Trautvetter Institut f¨urExperimentalphysik III, Ruhr-Universit¨atBochum, Bochum, Germany K. Suemmerer GSI Helmholtzzentrum f¨urSchwerionenforschung GmbH, Planckstraße 1, D-64291 Darmstadt, Germany S. Typel Excellence Cluster Universe, Technische Universit¨atM¨unchen,Boltzmannstraße 2, D-85748 Garching and GSI Helmholtzzentrum f¨urSchwerionenforschung GmbH, Planckstraße 1, D-64291 Darmstadt, Germany 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 3 for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to Reviews of Modern Physics 70 (1998) 1265. Contents 3. Transition to the ground state and 6.79 MeV in 15O 36 I. INTRODUCTION 3 4. Transition to the 6.17 MeV state 38 A. Solar Fusion II: the 2009/10 effort 4 5. Total S1 14(0) and conclusions 39 B. Contents of this review 5 B. Other CNO-cycle reactions 40 1. 12C(p; γ)13N 40 II. NUCLEAR REACTIONS IN 2. 15N(p; α)12C 40 15 16 HYDROGEN-BURNING STARS 6 3. N(p,γ) O 41 16 17 A. Rates and S-factors 7 4. O(p,γ) F 42 17 14 B. Screening of stellar and laboratory reactions 9 5. O(p,α) N 42 17 18 C. Fitting and extrapolating S-factors 10 6. O(p,γ) F 42 18 15 1. Theory constraints: model-based methods 11 7. O(p,α) N 42 2. Theory constraints: ab initio methods 12 3. Adopted procedures 13 XII. INDIRECT METHODS AND THEIR D. Treatment of uncertainties 14 VALIDATION 42 A. The asymptotic normalization coefficient method 43 III. THE pp REACTION 14 B. The Coulomb dissociation method 44 A. Progress in potential models 15 C. The Trojan Horse method 45 B. Progress in effective field theory (EFT) 15 D. Summary 45 1. Hybrid EFT (EFT*) 15 XIII. FUTURE FACILITIES AND CURRENT 2. Pionless EFT 16 CAPABILITIES 3. Comment on Mosconi et al. 16 46 C. Summary 16 A. Inverse kinematics measurements using recoil separators 46 IV. THE d(p,γ)3He RADIATIVE CAPTURE B. Underground facilities 47 REACTION 17 Acknowledgments and Dedication 50 A. Data sets 17 B. Theoretical studies 18 Appendix: Treating Uncertainties 50 C. Summary 18 A. Introduction 50 B. The inflation factor method 51 V. THE 3He(3He,2p)4He REACTION 18 C. Application of the inflation factor method 52 A. Data sets and fitting 19 D. Other methods 52 VI. THE 3He(α,γ)7Be REACTION 20 References 52 A. Experimental measurements 20 B. Theory 21 1. Model selection for S34(0) determination 22 2. Region of S34(E) fitting 22 I. INTRODUCTION 3. Theoretical uncertainty in the S34(0) determination 22 In 1998 the Reviews of Modern Physics published a 4. S-factor derivatives 22 summary and critical analysis of the nuclear reaction 5. Comment on phase shifts 22 C. S34(0) determination 23 cross sections important to solar burning. That effort, Adelberger et al. (1998) and denoted here as Solar Fu- 3 + 4 VII. THE He(p,e νe) He REACTION 24 sion I, began with a meeting hosted by the Institute for A. hep calculations 24 Nuclear Theory, University of Washington, 17-20 Febru- B. Summary 25 ary 1997. A group of international experts in the nuclear VIII. ELECTRON CAPTURE BY 7Be, pp, and CNO physics and astrophysics of hydrogen-burning stars met NUCLEI 26 to begin critical discussions of the existing data on rele- vant nuclear reactions, with the aim of determining \best IX. THE 7Be(p,γ)8B REACTION 28 A. The direct 7Be(p,γ)8B reaction 28 values" and uncertainties for the contributing low-energy 1. Beam-target overlap 28 S-factors. The group also considered opportunities for 2. 8B backscattering 29 further improvements in both measurements and theory. 3. Proton energy loss corrections 29 Such data and related nuclear theory have been cru- B. Theory 29 cial to the standard solar model (SSM) and the neutrino C. 8B Coulomb dissociation measurements 31 7 8 fluxes it predicts. Indeed, measurements of nuclear re- D. Direct Be(p,γ) B analysis and S17(0) determination 32 actions gave the field its start. In 1958 Holmgren and X. THE SPECTRUM OF 8B NEUTRINOS 34 Johnston (1958, 1959) showed that the rate for 3He+4He 7Be +γ was 1000 times larger than expected, and XI. THE CNO CYCLES 35 ! ∼ 4 A. The reaction 14N(p,γ)15O 35 thus that the pp chain for He synthesis would have addi- tional terminations beyond 3He+3He 4He + 2p. This 1. Current status and results 35 ! 2. R-matrix analysis and normalization 36 result led Davis to recognize that his chlorine detector 4 might be able to see the higher energy neutrinos from the dual discoveries of Super-Kamiokande (Fukuda et al., these other terminations, and spurred Bahcall and oth- 2001) and SNO (Ahmad et al., 2001) { two distinct neu- ers to develop a quantitative model of the Sun capable trino oscillations responsible for the missing atmospheric of predicting those fluxes (Bahcall and Davis Jr., 1982). and solar neutrinos, largely determining the pattern of At the time of the 1997 meeting, three decades of ef- the light neutrino masses. But issues remain, and most fort in solar neutrino physics had produced four measure- of these require precision. There is intense interest in ex- ments that were at variance with the SSM and the stan- tending direct measurements to the low-energy portion dard model of electroweak interactions. The measure- of the solar neutrino spectrum (< 2 MeV), where exper- ments came from the pioneering work of Ray Davis, Jr. iments with good energy resolution∼ can determine the (Davis Jr., 1994; Davis Jr. et al., 1968); the observation separate contributions of pep, CNO, 7Be, and pp neutri- of 8B neutrinos in the Kamiokande water Cerenkov de- nos. There is the potential to further constrain the solar tector (Fukuda et al., 1996); and the GALLEX (Kirsten neutrino mixing angle θ12: the solar luminosity deter- et al., 2003) and SAGE (Gavrin et al., 2003) radiochemi- mines the pp flux to high accuracy, and the low-energy cal detectors sensitive primarily to pp and 7Be neutrinos.
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