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Last Hope for an astrophysical solution to the solar neutrino problem

We discuss what appears the last hope for an astrophysical solution to the solar neutrino problem: a correlated variation of the astrophysical factors for the helium burning cross sections ($S_{33}$ and $S_{34}$) and either $S_{17}$ or the central temperature $T_c$. In this context, we recognize the important role played by the CNO neutrinos. In fact, we can obtain a fair fit to the experimental data only if three conditions are met simultaneously: the astrophysical factor $S_{33}$ is about 200 times what is presently estimated, the astrophysical factor $S_{17}$ is about 3 times larger and the $^{13}$N and $^{15}$O neutrino fluxes are negligible compared to the ones predicted by standard solar models. These conditions are not supported by the present data and their correlated combination is improbable.