Electron Correlations and Solar Neutrino Counts

Abstract

EXPERIMENTS to detect the neutrino flux from the Sun could be used to test the basic hypotheses concerning the internal constitution of the Sun and the nuclear fusion reactions believed to be occurring in its interior. The measurements of Davis, Harmer and Hoffmann¹ give an upper bound on the neutrino counting rate which is approximately half of the theoretical rate calculated by Bahcall, Bahcall and Shaviv², and an order of magnitude smaller than theoretical rates obtained by other authors. Before the discrepancy between theory and experiment can be accepted as requiring a radical change in the theory of stellar structure, it is first necessary to reduce the uncertainties and poor approximations contained in the “constitutive relations” of the theory; that is, in the equations for the nuclear reaction rates, the pressure and the opacity³, each expressed as a function of density, temperature and chemical composition of the medium. In current tables⁴ of solar opacity, the contribution from the scattering of radiation by free electrons is calculated under the unjustified assumption that the plasma of the solar interior can be treated as a perfect classical gas, and hence that the scattering cross-section is given simply by the classical frequency-independent Thomson cross-section N_eσ_t, for N_e independent electrons in the plasma. This report shows that corrections to σ_t produced by classical^5–7 and quantum⁶ electron correlations reduce the electron-scattering opacity in the core of the Sun by approximately one-third, and that this leads to a significant reduction in the theoretical neutrino flux.