Resonant Structures in $p{}^7\mathrm{Be}$ Scattering and Their Connection to the Astrophysical $S$-Factor

TL;DR

This study uses the Variable Phase Approach to analyze resonant structures in proton-7Be scattering, linking these resonances to peaks in the astrophysical S-factor, which are crucial for understanding stellar nucleosynthesis.

Contribution

It introduces the application of the Variable Phase Approach to identify resonance energies in 7Be+p scattering relevant to astrophysical S-factor calculations.

Findings

Resonant states correspond to peaks in partial cross sections.

Resonances significantly enhance the S-factor at low energies.

VPA effectively determines resonance energies in nuclear reactions.

Abstract

In this paper, we employ the Variable Phase Approach (VPA) to obtain the scattering phase shifts \( \delta(E, r) \), amplitude function \( A(r) \), and radial wavefunction \( u(r) \) for various channels involved in the astrophysical reaction \( {}^7\mathrm{Be}(p,\gamma)^8\mathrm{B} \). Using the extracted phase shifts, we compute the total and partial cross sections. It is observed that the peaks in the partial cross section correspond to resonant states in the compound nucleus, which also manifest as enhancements in the astrophysical S-factor. These resonances significantly increase the reaction probability at certain energies, particularly in the low-energy regime relevant to stellar nucleosynthesis. The VPA thus serves as a reliable and efficient method for calculating scattering phase shifts and, in turn, extracting the resonance energies of different partial waves. These resonance energies can provide valuable insight into the energy region where the astrophysical \textit{S}-factor is likely to peak.