This figure is Fig. 2 from the RMP paper by Adelberger et al. (1998) and is adapted from Fig. 9 of Junker et al. (1998), a recent paper by the LUNA Collaboration. The measured cross-section factor S(E) for the 3He (3He, 2p)4He reaction is shown and a fit with a screening potential Ue is illustrated. The Gamow peak at the solar central temperature is shown in arbitrary units. The data shown here correspond to a bare nucleus value at zero energy of S(0) = 5.4 MeV b and a value at the Gamow peak of S(Gamow Peak) = 5.3 MeV b.

Nuclear fusion reactions in the sun

The figure shows the principal reactions in the pp fusion chain in the sun. The BP2000 solar model was used to calculate the fraction of the terminations of the chain in which a given reaction participates. The neutrino energies contain small corrections due to thermal phenomena in the Sun.
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The luminosity constraint on solar neutrino fluxes
Author(s): John N. Bahcall
Journal: Phys. Rev. C., 65 (January 2002), 025801, hep-ph/0108148.

Abstract: A specific linear combination of the total solar neutrino fluxes must equal the measured solar photon luminosity if nuclear fusion reactions among light elements are responsible for solar energy generation. This luminosity constraint, previously used in a limited form in testing the no neutrino oscillation hypothesis, is derived in a generality that includes all of the relevant solar neutrino fluxes and which is suitable for analyzing the results of many different solar neutrino experiments. With or without allowing for neutrino oscillations, the generalized luminosity constraint can be used in future analyses of solar neutrino data. Accurate numerical values for the linear coefficients are provided.

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Solar Fusion Cross Sections

Authors: E. C. Adelberger, S. M. Austin, J. N. Bahcall, A. B. Balantekin, G. Bogaert, L. S. Brown, L. Buchmann, F. E. Cecil, A. E. Champagne, L. de Braeckeleer, C. A. Duba, S. R. Elliott, S. J. Freedman, M. Gai, G. Goldring, C. R. Gould, A. Gruzinov, W. C. Haxton, K. M. Heeger, E. Henley, C. W. Johnson, M. Kamionkowski, R. W. Kavanagh, S. E. Koonin, K. Kubodera, K. Langanke, T. Motobayashi, V. Pandharipande, P. Parker, R. G. H. Robertson, C. Rolfs, R. F. Sawyer, N. Shaviv, T. D. Shoppa, K. A. Snover, E. Swanson, R. E. Tribble, S. Turck-Chieze, and J. F. Wilkerson
Journal:Reviews of Modern Physics, 70, 1265-1292 (October 1998), astro-ph/9805121.

Abstract: We review and analyze the available information for nuclear fusion cross sections that are most important for solar energy generation and solar neutrino production. We provide best values for the low-energy cross-section factors and, wherever possible, estimates of the uncertainties. We also describe the most important experiments and calculations that are required in order to improve our knowledge of solar fusion rates.

The cross sections and uncertainties quoted in this paper have been used in the article ``How Uncertain Are Solar Neutrino Predictions?'' by J.N. Bahcall, S. Basu, and M. H. Pinsonneault, Phys. Lett. B, 433, 1-8 (August 1998), astro-ph 9805135, to determine the best-estimates and uncertainties in solar neutrino fluxes and sound speeds.

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The Salpeter Plasma Correction for Solar Fusion Reactions

Authors: John N. Bahcall, Lowell S. Brown, Andrei Gruzinov, and R. F. Sawyer
Journal: A&A, 383, 291-295 (2002), astro-ph/0010055.

Abstract: We review five different derivations that demonstrate that the Salpeter formula for the plasma corrections to fusion rates is valid at the center of the sun with insignificant errors (~ percent). We point out errors in several recent papers that have obtained a variety of answers, some even with the wrong sign or the wrong functional dependence.

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Screening in Thermonuclear Reaction Rates in the Sun

Authors:Andrei V. Gruzinov and John N. Bahcall
Journal:The Astrophysical Journal, 504, 996-1001 (September 10, 1998), astro-ph/9801028.

Abstract: We evaluate the effect of electrostatic screening by ions and electrons on low-Z thermonuclear reactions in the sun. We use a mean field formalism and calculate the electron density of the screening cloud using the appropriate density matrix equation of quantum statistical mechanics. Because of well understood physical effects that are included for the first time in our treatment, the calculated enhancement of reaction rates does not agree with the frequently used interpolation formulae. Our result does agree, within small uncertainties, with Salpeter's weak screening formula. If weak screening is used instead of the commonly employed screening prescription of Graboske et al., the predicted 8B neutrino flux is increased by 7% and the predicted chlorine rate is increased by 0.4 SNU.

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The Proton-Proton Reaction, Solar Neutrinos, and a Relativistic Field Theoretic Model of the Deuteron

Authors: J. N. Bahcall and Marc Kamionkowski
Journal:Nuclear Physics A, 625, No. 4, 893-895 (November 10, 1997); astro-ph/9707320.

Abstract: In a series of recent papers, Ivanov et al. and Oberhummer et al. have calculated the rate for the p + p d + e+ + e reaction with a zero-range four-fermion effective interaction and find a result 2.9 times higher than the standard value calculated from non-relativistic potential theory. Their procedure is shown to give a wrong answer because their assumed interaction disagrees with low-energy pp scattering data.

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The 7Be Electron Capture Rate in the Sun

Authors: Andrei V. Gruzinov and John N. Bahcall
Journal: The Astrophysical Journal, 490, 437-441 (November 20, 1997); astro-ph/9702065.

Abstract: For solar conditions, we numerically integrate the density matrix equation for a thermal electron in the field of a 7Be ion and other plasma ions and smeared-out electrons. Our results are in agreement with previous calculations that are based on a different physical picture, a picture which postulates the existence of distinct continuum and bound state orbits for electrons. The density matrix calculation of the electron capture rate is independent of the nature of electron states in the solar plasma. To within a 1% accuracy, the effects of screening can be described at high temperatures by a Salpeter-like factor of exp (-Ze2/kTRD), which can be derived from the density matrix equation. The theoretical uncertainty in the electron capture rate is about ± 2%.

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Electron-Screening Correction for the Proton-Proton Reaction

Authors: John N. Bahcall, Xuelei Chen, and Marc Kamionkowski
Journal: Physical Review C (Brief Reports), 57, 2756-2759 (May 1998); astro-ph/9612209.

Abstract: We test the Salpeter formalism for calculating electron screening of nuclear fusion reactions by solving numerically the relevant Schrodinger equation for the fundamental proton-proton reaction. We evaluate exactly the square of the overlap integral of the two-proton wave function and the deuteron wave function and compare with the usual analytic approximation. The usual WKB solution agrees with the numerical solution to O(10-4).

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Temperature Dependence of Solar Neutrino Fluxes

Authors: John N. Bahcall and Andrew Ulmer
Journal: Physical Review D, 53, 4202-4225 (April 15, 1996); astro-ph/9602012.

Abstract: Using a one-zone model of the Sun, we derive expressions for the temperature dependence of the solar neutrino fluxes. The exponents of the scaling laws agree to within 20 percent or better with the exponents extracted from detailed solar models.

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Central Temperature of the Sun Can be Measured via the 7Be Solar neutrino Line
Author(s): John N. Bahcall
Journal: Physical Review Letters, 71, 2369-2371 (October 11, 1993) hep-ph/9309292.

Abstract: A precise test of the theory of stellar evolution can be performed by measuring the difference in average energy between the neutrino line produced by 7Be electron capture in the solar interior and the corresponding neutrino line produced in a terrestrial laboratory. The high temperatures in the center of the sun broaden the line asymmetrically, FWHM = 1.6 keV, and cause an average energy shift of 1.3 keV. The width of the 7Be neutrino line should be taken into account in calculations of vacuum neutrino oscillations.

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Solar Neutrinos: Where We Are, What We Need

Authors:John N. Bahcall
Journal: In Few-Body Problems in Physics. Proceedings of the 15th International Conference on Few-Body Problems in Physics, Groningen, The Netherlands, 22-26 July 1997, ed. J. C. S. Bacelar, A. E. L. Dieperink, and R. A. Malfliet (Amsterdam: Elsevier Science Publishers), Nuclear Physics A, 631, 29c--41c (1998), nucl-th/9802050.

Abstract: This talk was given at the 5th International Conference on Few-Body Problems in Physics, Groningen, The Netherlands. I describe the five most important nuclear physics problems whose solution is required for understanding the precise implications of solar neutrino experiments, as well as compare the standard model predictions with solar neutrino experiments and with helioseismological measurements.

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Line Versus Continuum Solar Neutrinos

Author(s): John N. Bahcall
Journal: Phys. Rev. D, 41, 2964-2966 (15 May 1990)

Abstract: The rate of neutrino line emission is calculated for nuclei that are usually assumed to produce only continuum neutrino emission. A convenient formula is derived that gives for solar interior conditions the ratio of the rates of neutrino line emission to continuum neutrino emission. The only significant line emission from the solar interior is expected from the pep and 7Be-electron capture reactions.

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Do hep neutrinos affect the solar neutrino energy spectrum ?

Author(s): John N. Bahcall, Plamen I. Krastev
Journal:Physics Letters B, 436/3-4, 243-250 (September 24, 1998), hep-ph/9807525

Abstract:If the low energy cross section for 3He + p--> 4He + e+ + nue, the `hep' reaction, is  >~  20 times larger than the best (but uncertain) theoretical estimates, then this reaction could significantly influence the electron energy spectrum produced by solar neutrino interactions and measured in the SuperKamiokande, SNO, and ICARUS experiments. We compare predicted energy spectra for different assumed hep fluxes and different neutrino oscillation scenarios with the observed SuperKamiokande spectrum. The spectra with enhanced hep contributions provide better fits to the SuperKamiokande data.

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