Coulomb tunneling for fusion reactions in dense matter: Path integral Monte Carlo versus mean field

We compare Path Integral Monte Carlo calculations by Militzer and Pollock (Phys. Rev. B 71, 134303, 2005) of Coulomb tunneling in nuclear reactions in dense matter to semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean-field potential. We find a very good agreement of two approaches at temperatures higher than ~1/5 of the ion plasma temperature. We obtain a simple parameterization of the mean field potential and of the respective reaction rates. We analyze Gamow-peak energies of reacting ions in various reaction regimes and discuss theoretical uncertainties of nuclear reaction rates taking carbon burning in dense stellar matter as an example.Comment: 13 pages, 7 figures, to appear in Phys. Rev.

Weakly screened thermonuclear reactions in astrophysical plasmas: Improving Salpeter's model

This paper presents a detailed study of the electron degeneracy and nonlinear screening effects which play a crucial role in the validity of Salpeter's weak-screening model. The limitations of that model are investigated and an improved one is proposed which can take into account nonlinear screening effects. Its application to the solar pp reaction derives an accurate screening enhancement factor and provides a very reliable estimation of the associated neutrino flux uncertanties.Comment: 23 RevTex pages + 4 ps figures. (No revision,just adding URL link). Accepted for publication in Europ.Phys.J.A. See http://link.springer.de/link/service/journals/10105/index.ht

Non-linear screening corrections of stellar nuclear reaction rates and their effects on solar neutrino fluxes

Non-linear electron screening corrections of stellar nuclear fusion rates are calculated analytically in the framework of the Debye-Huckel model and compared with the respective ones of Salpeter's weak screening approximation. In typical solar conditions, the deviation from Salpeter's screening factor is less than one percent, while for hotter stars such corrections turn out to be of the order of one percent only over the limits of the Debye-Huckel model. Moreover, an investigation of the impact of the derived non-linear screening effects on the solar neutrino fluxes yields insignificant corrections for both the pp and CNO chain reactions.Comment: To appear in Phys.Rev.

The role of electron-screening deformations in solar nuclear fusion reactions and the solar neutrino puzzle

Thermonuclear fusion reaction rates in the solar plasma are enhanced by the presence of the electron cloud that screens fusing nuclei. The present work studies the influence of electron screening deformations on solar reaction rates in the framework of the Debye-Huckel model. These electron-ion cloud deformations, assumed here to be static and axially symmetric, are shown to be able to considerably influence the solar neutrino fluxes of the pp and the CNO chains, with reasonable changes in the macroscopic parameters of the standard solar model (SSM) . Various known deformation sources are discussed but none of them is found strong enough to have a significant impact on the SSM neutrino fluxes.Comment: Revised version (14 RevTeX pages, 3 ps figures). Accepted for publication in Nuclear Physics

Determination of plasma screening effects for thermonuclear reactions in laser-generated plasmas

Due to screening effects, nuclear reactions in astrophysical plasmas may behave differently than in the laboratory. The possibility to determine the magnitude of these screening effects in colliding laser-generated plasmas is investigated theoretically, having as a starting point a proposed experimental setup with two laser beams at the Extreme Light Infrastructure facility. A laser pulse interacting with a solid target produces a plasma through the Target Normal Sheath Acceleration scheme, and this rapidly streaming plasma (ion flow) impacts on a secondary plasma created by the interaction of a second laser pulse on a gas jet target. We model this scenario here and calculate the reaction events for the astrophysically relevant reaction $^{13}$C($^4$He, $n$)$^{16}$O. We find that it should be experimentally possible to determine the plasma screening enhancement factor for fusion reactions by detecting the difference in reaction events between two scenarios of ion flow interacting with the plasma target and a simple gas target. This provides a way to evaluate nuclear reaction cross-sections in stellar environments and can significantly advance the field of nuclear astrophysics.Comment: 9 pages, 4 figures, 4 tables; minor changes made, accepted by The Astrophysical Journa

Standard Solar Neutrinos

An improved standard solar model has been used to calculate the fluxes of standard solar neutrinos. It includes premain sequence evolution, element diffusion, partial ionization effects, and all the possible nuclear reactions between the main elements. It uses updated values for the initial solar element abundances, the solar age, the solar luminosity, the nuclear reaction rates and the radiative opacities. Neither nuclear equilibrium, nor complete ionization are assumed. The calculated solar neutrino fluxes are compared with published results from the four solar neutrino experiments. The calculated $^8$B solar neutrino flux is consistent, within the theoretical and experimental uncertainties, with the solar neutrino observations at Homestake and Kamiokande. The observations suggest that the $^7$Be solar neutrino flux is much smaller than that predicted. However, conclusive evidence for the suppression of the $^7$Be solar neutrino flux will require experiments like BOREXINO and HELLAZ. If the $^7$Be solar neutrino flux is suppressed, it still can be due either to standard physics and astrophysics or neutrino properties beyond the standard electroweak model. Only future neutrino experiments, such as SNO, Superkamiokande, BOREXINO and HELLAZ, will be able to show that the solar neutrino problem is a consequence of neutrino properties beyond the standard electroweak model.Comment: To be published in ApJ. Vol. 468 (1996

Screening in Thermonuclear Reaction Rates in the Sun

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 $^8$B neutrino flux is increased by 7% and the predicted chlorine rate is increased by 0.4 SNU.Comment: 15 pages, 1 figure, submitted to ApJ. Acknowledgments, a footnote, and an explanation added. Additional information at www.sns.ias.edu/~jn

Final Evolution and Delayed Explosions of Spinning White Dwarfs in Single Degenerate Models for Type Ia Supernovae

We study the occurrence of delayed SNe~Ia in the single degenerate (SD) scenario. We assume that a massive carbon-oxygen (CO) white dwarf (WD) accretes matter coming from a companion star, making it to spin at the critical rate. We assume uniform rotation due to magnetic field coupling. The carbon ignition mass for non-rotating WDs is M_{ig}^{NR} \approx 1.38 M_{\odot}; while for the case of uniformly rotating WDs it is a few percent larger (M_{ig}^{R} \approx 1.43 M_{\odot}). When accretion rate decreases, the WD begins to lose angular momentum, shrinks, and spins up; however, it does not overflow its critical rotation rate, avoiding mass shedding. Thus, angular momentum losses can lead the CO WD interior to compression and carbon ignition, which would induce an SN~Ia. The delay, largely due to the angular momentum losses timescale, may be large enough to allow the companion star to evolve to a He WD, becoming undetectable at the moment of explosion. This scenario supports the occurrence of delayed SNe~Ia if the final CO WD mass is 1.38 M_{\odot} < M < 1.43 M_{\odot}. We also find that if the delay is longer than ~3 Gyr, the WD would become too cold to explode, rather undergoing collapse.Comment: 6 pages, 5 figures, published in the Astrophysical Journal Letters, 809, L6 (2015), added some corrections for errat