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A new analysis of the precise experimental astrophysical $S$-factors for thedirect capture $^3He(\alpha,\gamma)^7{\rm {Be}}$ reaction [B.S. Nara Singh etal., Phys.Rev.Lett. {\bf 93} (2004) 262503; D. Bemmerer et al., Phys.Rev.Lett.{\bf 97} (2006) 122502; F.Confortola et al., Phys.Rev. {\bf C 75} (2007) 065803and T.A.D.Brown et al., Phys.Rev. {\bf C 76} (2007) 055801] populating to theground and first excited states of $^7{\rm Be}$ is carried out based on themodified two - body potential approach in which the direct astrophysical$S$-factor, $S_{34}(E)$, is expressed in terms of the asymptotic normalizationconstants for $^3{\rm {He}}+\alpha\to ^7{\rm {Be}}$ and two additionalconditions are involved to verify the peripheral character of the reactionunder consideration. The Woods--Saxon potential form is used for the bound($\alpha+^3{\rm {He}}$)- state and the $^3{\rm {He}}\alpha$- scattering wavefunctions. New estimates are obtained for the "indirectly measured", values ofthe asymptotic normalization constants (the nuclear vertex constants) for$^3{\rm {He}}+\alpha\to^7{\rm {Be}}(g.s.)$ and $^3{\rm {He}}+\alpha\to^7{\rm{Be}}(0.429 MeV)$ as well as the astrophysical $S$-factors $S_{34}(E)$ atE$\le$ 90 keV, including $E$=0. The values of asymptotic normalizationconstants have been used for getting information about the $\alpha$-particlespectroscopic factors for the mirror ($^7Li^7{\rm {Be}}$)-pair.

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