The $^6$Li$(p, \gamma)^7$Be reaction rate in the light of the new LUNA data

TL;DR

This paper provides new calculations of the $^{6}$Li$(p, extgamma)^{7}$Be reaction rate using a modified potential cluster model, aligning well with recent LUNA data and suggesting updates to existing nuclear reaction databases.

Contribution

The study introduces a modified potential cluster model with forbidden states for calculating the $^{6}$Li$(p, extgamma)^{7}$Be reaction rate, incorporating recent experimental data and low-lying resonances.

Findings

The $S(0)$ value is estimated at 101 eV·b.

The calculated reaction rates agree with LUNA data for low energies.

Recommendations are made to update NACRE and NACRE II databases.

Abstract

We present new calculations of the astrophysical $S-$factor and reaction rate for the $^{6}$Li$(p,\gamma )^{7}$Be reaction at energies of 10 keV to 5 MeV in the framework of a modified potential cluster model with forbidden states, including low lying resonances. The astrophysical $S(E)-$factor is compared with the available experimental data and calculations done within different models. The results for the $S-$factor are in good agreement with the data set (for $E<0.3$ MeV) and calculations (for $E<0.6$ MeV) of LUNA collaboration (Phys. Rev. C 102$,$ 052802, 2020). The recommended extrapolated zero value $S(0)$ turned out to be 101 eV $\cdot $ b. Using the theoretical total cross-sections$,$ the $^{6}$Li$(p,\gamma)^{7} $Be capture reaction rate is calculated at temperatures ranging from 0.01 to 10 $T_{9}$ and compared with NACRE and NACRE II. Analytical expressions for the $S-$factor and reaction rate are given, and the effect of low-lying resonances on the reaction rate is estimated. We suggest to update the NACRE and NACRE II databases in light of the new LUNA data and present calculations.