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The solar neutrino problem

The solar neutrino problem had origin from the discrepancy between the expectations of the solar $\nu_e$ flux, as calculated by the Solar Standard Model, and the experimental results.

But even if we forget the Solar Model and we study the compatibility among the available experimental data we find an internal inconsistency. In Table [*] the experimental results are quoted; they constraint in different ways the neutrino fluxes from the various sources. A fourth equation can be written taking into account the constraints introduced by the solar luminosity.

Experiment Measured flux
S.M. expectation
Homestake 0.27$\pm$0.06 0.814 $S_c=\Sigma\sigma_{L,c}\phi_i$
Kamiokande 0.44$\pm$0.06 7.5 $S_k=\sigma_k \phi(B)$
Gallium (Gallex, Sage) 0.5 $\pm$ 0.06 0.235 $S_q=\Sigma\sigma_{i,q}\phi_i$
Luminosity     $ K=\Sigma (Q/2+<E>_i)Q_i$

The Kamiokande results, due to its high threshold, constraint only the neutrino flux from8B. Homestake and Gallium experiments involve also lower energy neutrino fluxes.

If we try to extract the 7Be neutrino flux from the four equations of Table [*] we obtain a flux negative or very close to zero. In any case the $\nu$ flux from 7Be appears to be smaller than the 8B flux.

This is in strong contradiction with the sequence of the nuclear reactions within the Sun, where the reaction involving 7Be precedes the reaction involving 8B and thus the 7Be nuclides are in some ways the father than 8B. This is the paradox of the present situation of the Solar neutrino problem. 

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