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

TL;DR

This paper refines the calculation of astrophysical S-factors for the $^7Be(p,\, ext{γ})^8B$ reaction at solar energies using a modified potential approach, providing new estimates for nuclear vertex constants and scattering parameters.

Contribution

It introduces a modified two-body potential method to analyze experimental S-factors, yielding improved estimates of asymptotic normalization constants and scattering parameters for the reaction.

Findings

New estimates of asymptotic normalization constants for $p+^7Be\to ^8B$

Refined values of $S_{17}(E)$ at energies up to 115 keV

Determination of $s$-wave scattering length and $p$-wave effective range

Abstract

A new analysis of the precise experimental astrophysical S-factors for the direct capture $^7Be(p,\gamma)$ $^8B$ 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, $ {\rm S_{17}(E)}$, is expressed in terms of the asymptotic normalization constants for $p+^7Be\to ^8B$ 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 ($p+^7Be$)- state wave function and for the $p^7Be$- 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 $p+^7Be\to ^8B$ 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 $p^7Be$- scattering.