The state of ⁷Be in the core of the Sun and the solar neutrino flux

The exact ionization state of ⁷Be in the solar core is crucial for the precise prediction of the solar ⁸B neutrino flux. We therefore examine the effect of pressure ionization on the ionization state of ⁷Be 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 neighbour on the electronic structure of a given ion. To this goal, we first solve the Schrödinger 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 wavefunction 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 ⁷Be + e^- reaction is reduced by 20-30 per cent, depending on the details of the solar model. Because ⁷Be is a trace element, its total production is controlled by the unchanged ⁴He -³ He 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 ⁷Be increases and with it the ⁸B neutrino flux. The increase in Ø_V(⁸B) is by about 20-30 per cent. The neutrino flux due to ⁷Be 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 Ø_v(⁸B) Ø_v( ⁷Be) changes as well.