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

Igamov, S. B.; Tursunmakhatov, K. I.; Yarmukhamedov, R.

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

Authors

Igamov, S. B.

Tursunmakhatov, K. I.

Yarmukhamedov, R.

Description

A new analysis of the precise experimental astrophysical $S$-factors for the direct capture $^3He(α,γ)^7{\rm {Be}}$ reaction [B.S. Nara Singh et al., 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) 065803 and T.A.D.Brown et al., Phys.Rev. {\bf C 76} (2007) 055801] populating to the ground and first excited states of $^7{\rm Be}$ is carried out based on the modified two - body potential approach in which the direct astrophysical $S$-factor, $S_{34}(E)$, is expressed in terms of the asymptotic normalization constants for $^3{\rm {He}}+α\to ^7{\rm {Be}}$ and two additional conditions are involved to verify the peripheral character of the reaction under consideration. The Woods--Saxon potential form is used for the bound ($α+^3{\rm {He}}$)- state and the $^3{\rm {He}}α$- scattering wave functions. New estimates are obtained for the "indirectly measured", values of the asymptotic normalization constants (the nuclear vertex constants) for $^3{\rm {He}}+α\to^7{\rm {Be}}(g.s.)$ and $^3{\rm {He}}+α\to^7{\rm {Be}}(0.429 MeV)$ 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 ($^7Li^7{\rm {Be}}$)-pair.
27 pages, 11 figures, 2 tables