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Determination of the 3He+alpha\to 7Be asymp. normalization coefficients (nucl. vertex constants) and their application for extrapolation of the 3He(alpha,gamma)7Be astroph. S-factors to the solar energy region

A new analysis of the modern precise measured astrophysical $S$ factors for the direct capture $^3He(α,γ)^7{\rm {Be}}$ reaction [B.S. Nara Singh {\it et al.}, Phys.Rev.Lett. {\bf 93}, 262503 (2004); D. Bemmerer {\it et al.}, Phys.Rev.Lett. {\bf 97}, 122502 (2006); F.Confortola {\it et al.}, Phys.Rev.C {\bf 75}, 065803 (2007), T.A.D.Brown {\it et al.}, Phys.Rev. C {\bf 76}, 055801 (2007) and A Di Leva, {\it et al.},Phys.Rev.Lett. {\bf 102}, 232502 (2009)] populating to the ground and first excited states of $^7{\rm Be}$ is carried out based on the modified two - body potential approach. New estimates are obtained for the $^{\glqq}$indirectly determined\grqq\, values of the asymptotic normalization constants (the nuclear vertex constants) for $^3{\rm {He}}+α\to{\rm {^7Be}}$(g.s.) and $^3{\rm {He}}+α\to{\rm {^7Be}}$(0.429 MeV) as well as the astrophysical $S$ factors $S_{34}(E)$ at E$\le$ 90 keV, including $E$=0. The values of asymptotic normalization constants have been used for getting information about the $α$-particle spectroscopic factors for the mirror (${\rm{^7Li}}{\rm {^7Be}}$)-pair.