The electron-capture rate on $^7$Be is the main production channel for $^7$Li in several astrophysical environments. Theoretical evaluations have to account for not only the nuclear interaction, but also the processes in the plasma where $^7$Be ions and electrons interact. In the past decades several estimates were presented, pointing out that the theoretical uncertainty in the rate is in general of few percents. In the framework of fundamental solar physics, we consider here a recent evaluation for the $^7$Be+e$^-$ rate, not used up to now in the estimate of neutrino fluxes. We analysed the effects of the new assumptions on Standard Solar Models (SSMs) and compared the results obtained by adopting the revised $^7$Be+e$^-$ rate to those obtained by the one reported in a widely used compilation of reaction rates (ADE11). We found that new SSMs yield a maximum difference in the efficiency of the $^7$Be channel of about -4% with respect to what is obtained with the previously adopted rate. This fact affects the production of neutrinos from $^8$B, increasing the relative flux up to a maximum of 2.7%. Negligible variations are found for the physical and chemical properties of the computed solar models. The agreement with the SNO measurements of the neutral current component of the $^8$B neutrino flux is improved.
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