The p - p-chain reaction He-3(alpha, gamma)Be-7 can sensitively influence the prediction of the Be-7 and B-8 neutrino fluxes. Despite its importance, the knowledge of its reaction cross section at energies of the core of the Sun (15 keV - 30 keV) is limited and the accuracy far from the desired similar to 3% level. In the present paper the indirect measurement of the external capture contribution using the asymptotic normalization coefficient (ANC) technique is reported. The angular distributions of deuterons emitted in the Li-6(He-3,d)Be-7 alpha-transfer reactions were measured and the ANCs extracted from the scaling of distorted-wave Born approximation (DWBA) and coupled-channel (CC) calculations. Then, the astrophysical S-factor for the He-3(alpha, gamma)Be-7 reaction was calculated assuming E1 direct capture and the zero energy value turned out to be 0.534 +/- 0.025 keVb. Both our experimental and theoretical approaches were benchmarked through the analysis of the Li-6(p,gamma)Be-7 astrophysical factor, with interesting astrophysical applications to the understanding of the primordial lithium problem. In particular, the present work disfavors the occurrence of a claimed 200 keV resonance in the astrophysical factor.
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