Relativistic equilibrium velocity distribution, nuclear fusion reaction rate and the solar neutrino problem

Abstract

In solar interior, it is the equilibrium velocity distribution of few high-energy protons and nuclei that participates in determining nuclear fusion reaction rates. So, it is inappropriate to use the Maxwellian velocity distribution to calculate the rates of solar nuclear fusion reactions. We have to use the relativistic equilibrium velocity distribution for the purpose. The nuclear fusion reaction rate based on the relativistic equilibrium velocity distribution has a reduction factor with respect to that based on the Maxwellian distribution. The reduction factor depends on the temperature, reduced mass and atomic numbers of the studied nuclear fusion reactions, in other words, it varies with the sort of neutrinos. Substituting the relativistic equilibrium velocity distribution for the Maxwellian distribution is not important for the calculation of solar sound speeds. The relativistic equilibrium velocity distribution, if adopted in standard solar models, will lower solar neutrino fluxes and change solar neutrino energy spectra but maintain solar sound speeds. This velocity distribution is possibly a solution to the solar neutrino problem.