The primordial abundance of 7Li as predicted by Big Bang Nucleosynthesis (BBN) is more than a factor 2 larger than what has been observed in metal-poor halo stars. Herein, we analyze the possibility that this discrepancy originates from incorrect assumptions about the nuclear reaction cross sections relevant for BBN. To do this, we introduce an efficient method to calculate the changes in the 7Li abundance produced by arbitrary (temperature dependent) modifications of the nuclear reaction rates. Then, considering that 7Li is mainly produced from 7Be via the electron capture process 7Be + e -> 7Li + nu_e, we assess the impact of the various channels of 7Be destruction. Differently from previous analysis, we consider the role of unknown resonances by using a complete formalism which takes into account the effect of Coulomb and centrifugal barrier penetration and that does not rely on the use of the narrow-resonance approximation. As a result of this, the possibility of a nuclear physics solution to the 7Li problem is significantly suppressed. Given the present experimental and theoretical constraints, it is unlikely that the 7Be + n destruction rate is underestimated by the 2.5 factor required to solve the problem. We exclude, moreover, that resonant destruction in the channels 7Be + t and 7Be + 3He can explain the 7Li puzzle. New unknown resonances in 7Be + d and 7Be + alpha could potentially produce significant effects. Recent experimental results have ruled out such a possibility for 7Be+d. On the other hand, for the 7Be + alpha channel very favorable conditions are required. The possible existence of a partially suitable resonant level in 11C is studied in the framework of a coupled-channel model and the possibility of a direct measurement is considered.
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