The event rates and their recognized uncertainties are calculated for eleven solar neutrino experiments using accurate solar models. The same solar models are used to evaluate the frequency spectrum of the $p$ and $g$ oscillation modes of the sun and to compare with existing observations. A numerical table of the characteristics of the standard solar model is presented. Improved values have been calculated for all of the neutrino absorption cross sections evaluating the uncertainties for each neutrino source and detector as well as the best estimates. The neutrino capture rate calculated from the standard solar model for the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ experiment is 7.9(1±0.33) SNU, which spans the total theoretical range; the rate observed by Davis and his associates is (2.0±0.3) SNU. The ratio of the observed to the predicted flux at Earth of neutrinos from ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ decay lies in the range $0\le \left[\frac{\varphi {\left({}_{}{}^8{}_{}{}^{}\mathrm{B}\right)}_{\mathrm{observed}}}{\varphi {\left({}_{}{}^8{}_{}{}^{}\mathrm{B}\right)}_{\mathrm{predicted}}}\right]\le 0.5$. The recent results from the Kamiokande II electron scattering experiment confirm this conclusion. This discrepancy between calculation and observation is the solar neutrino problem. Measurements of the energy spectrum of solar neutrinos can discriminate between suggested solutions of the solar neutrino problem. Nonstandard solar models, many examples of which are also calculated in this paper, preserve the shape of the energy spectrum from individual neutrino sources, whereas most proposed weak-interaction explanations imply altered neutrino energy spectra. Detailed energy spectra of individual neutrino sources are presented as well as a composite solar neutrino spectrum. hep neutrinos from the ${}_{}{}^3{}_{}{}^{}\mathrm{He}+p$ reaction, probe a different region of the solar interior than do ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ neutrinos. Measurements of the very rare but highest-energy hep neutrinos are possible in proposed experiments using electron scattering, ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ detectors. The standard solar model predicts $p$-mode oscillation frequencies that agree to within about 0.5% with the measured frequencies and reproduce well the overall dispersion relation of the modes. However, there are several small but significant discrepancies between the measured and observed frequencies. The complementarity of helioseismology and solar neutrino experiments is demonstrated by constructing a solar model with a drastically altered nuclear energy generation that eliminates entirely the important high-energy ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ neutrinos, but which affects by less than 0.01% the calculated $p$-mode oscillation frequencies.

DOI:https://doi.org/10.1103/RevModPhys.60.297