Multi-Model Analysis of the Astrophysical $S(E)$ Factor for the ${}^9\mathrm{Be}(p,\alpha {)}^6\mathrm{Li}$ Reaction and Its Impact on Astrophysical Reaction Rates

Abstract

The ${}^9\mathrm{Be}(p,\alpha {)}^6\mathrm{Li}$ reaction is a destruction process for ${}^9\text{Be}$ in stars and the Big Bang. The Trojan Horse Method (THM) is a well-established indirect technique that enables the determination of reaction cross sections within the Gamow energy region while avoiding the uncertainties associated with low-energy extrapolations of the $S(E)$ factor and electron-screening effects. In this work, the bare-nucleus THM data reported by Wen \textit{et al.} are systematically analyzed using polynomial fitting, a double Breit--Wigner model, and the $R$-matrix formalism. The applicability and physical implications of these theoretical approaches in describing the low-energy $S(E)$ factor of the ${}^9\mathrm{Be}(p,\alpha {)}^6\mathrm{Li}$ reaction are investigated and compared. Since the THM data have been incorporated into the NACRE II reaction-rate compilation, leading to improved accuracy in reaction-rate evaluations, the refined theoretical analysis presented here provides further insight into the underlying reaction dynamics and establishes a more reliable foundation for stellar reaction-rate calculations. The results obtained in this work offer valuable reference for future high-precision experimental investigations and the development of theoretical models in nuclear astrophysics.