Analysis of the ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ astrophysical direct capture reactions in a modified potential-model approach

Abstract

Astrophysical $S$ factors and reaction rates of the direct radiative capture processes ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$, as well as the primordial abundance of the ${}^7\mathrm{Li}$ element, are estimated in the framework of a modified two-body potential model. It is shown that suitable modification of phase-equivalent $\alpha {-}^3\mathrm{He}$ potentials in the $d$ waves can improve the description of the astrophysical $S$ factor for the direct ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ radiative capture reaction at energies above 0.5 MeV. An estimated ${}^{7}Li/H$ abundance ratio of $(4.89\pm 0.18)\times 10^{-10}$ is in very good agreement with the recent measurement of $(5.0\pm 0.3)\times 10^{-10}$ by the LUNA collaboration.

Comments: 22 pages, 10 figures