  Heavy element and helium diffusion are both included for the first time in
this series of papers on precise solar models, along with improvements in the
input data for nuclear reaction rates, the solar luminosity, the solar age,
heavy element abundances, radiative opacities, helium and metal diffusion
rates, and neutrino interaction cross sections. The calculated neutrino event
rates, including all of the improvements, are $9.3_{-1.4}^{+1.2}$ SNU for the
\hbox{$^{37}$Cl} experimentand $137_{-7}^{+8} $ SNU for the \hbox{$^{71}$Ga}
experiments. The calculated flux of \hbox{$^{7}$Be} neutrinos is
$5.1(1.00_{-0.07}^{+0.06}) \times 10^{9}~{\rm cm^{-2}s^{-1}}$ and the flux of
${\rm ^8B}$ neutrinos is $6.5 (1.00_{-0.17}^{+0.14})\times 10^{6}~{\rm
cm^{-2}s^{-1}}$. The present-day surface helium abundance of the model is $Y_s
= 0.247$, in agreement with the helioseismological measurement of $Y_s = 0.242
\pm 0.003$ determined by Hernandez and Christensen-Dalsgaard (1994). The
computed depth of the convective zone is \hbox{$R = 0.712~ R_{\odot}$} in
agreement with the observed value determined from $p$-mode oscillation data of
\hbox{$R = 0.713 \pm 0.003~ R_{\odot}$} found by Christensen-Dalsgaard {\it et
al.}~(1991). Solar models that do not include diffusion disagree with the
helioseismology measurements. Although the present results increase the
predicted event rate in the four operating solar neutrino experiments by almost
$1\sigma$ (theoretical uncertainty), they only slightly increase the difficulty
of explaining the existing experiments with standard physics (i.e., by assuming
that nothing happens to the neutrinos after they are created in the center of
the sun).

High Energy Physics - Phenomenology;Astrophysics;Nuclear Theory