  The exact ionization state of Be7 in the solar core is crucial for the
precise prediction of the solar B8 neutrino flux. We therefore examine the
effect of pressure ionization on the ionization state of Be7 and all elements
with 12 >= Z >= 4. We show that under the conditions prevailing in the solar
core, one has to consider the effect of the nearest neighbor on the electronic
structure of a given ion. To this goal, we first solve the Schroedinger and
then the Kohn-Sham equations for an ion immersed in a dense plasma under
conditions for which the mean interparticle distance is smaller than the Debye
radius. The question of which boundary conditions should be imposed on the wave
function is discussed, examined and found to be crucial.
  Contrary to previous estimates showing that Beryllium is partially ionized,
we find that it is fully ionized. As a consequence, the predicted rate of the
Be7 + e- reaction is reduced by 20-30%, depending on the exact solar model.
Since Be7 is a trace element, its total production is controlled by the
unchanged He4+He3 reaction rate, and its destruction is determined by the rate
of electron capture. As the latter rate decreases when the Beryllium is fully
ionized (relative to the case of partially ionized Be), the estimate for the
abundance of Be7 increases and with it the B8 neutrino flux. The increase in
phi_nu(B8) is by about 20-30%. The neutrino flux due to Be7 electron capture
remains effectively unchanged because the change in the rate is compensated for
by a change in the abundance. Hence the prediction for the ratio of phi_nu(B8)
/ phi_nu(Be7) changes as well.
