Asymptotic normalization coefficients (nuclear vertex constants) for $p{+}^{7}Be{\to }^{8}B$ and the direct ${}^{7}Be(p,\gamma {)}^{8}B$ astrophysical S-factors at solar energies

Abstract

A new analysis of the precise experimental astrophysical S-factors for the direct capture ${}^{7}Be(p,\gamma )$ ${}^{8}B$ reaction [A.J.Junghans et al.Phys.Rev. C 68 (2003) 065803 and L.T. Baby et al. Phys.Rev. C 67 (2003) 065805] is carried out based on the modified two - body potential approach in which the direct astrophysical S-factor, ${\mathrm{S}}_{17}(\mathrm{E})$, is expressed in terms of the asymptotic normalization constants for $p{+}^{7}Be{\to }^{8}B$ 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 ($p{+}^{7}Be$)- state wave function and for the $p^{7}Be$- scattering wave function. New estimates are obtained for the $^{\glqq}$indirectly measured\grqq values of the asymptotic normalization constants (the nuclear vertex constants) for the $p{+}^{7}Be{\to }^{8}B$ and $S_{17}(E)$ at E$\le$ 115 keV, including $E$=0. These values of $S_{17}(E)$ and asymptotic normalization constants have been used for getting information about the $^{\glqq}$indirectly measured\grqq values of the $s$ wave average scattering length and the $p$ wave effective range parameters for $p^{7}Be$- scattering.

27 pages, 6 figures