Investigating the rate of $$^{10}$$ Be(n, $$\gamma$$ ) $$^{11}$$ Be radiative capture reaction within the FRDWBA framework

This study examines the radiative capture of a neutron by \(^{10}\)Be using the Coulomb dissociation approach within the FRDWBA theory. We analyze the elastic Coulomb breakup of \(^{11}\)Be on a \(^{208}\)Pb target at 72 MeV/A to determine the photodisintegration cross section and radiative capture cross section. Utilizing the Maxwell-averaged velocity distribution, we calculate the resulting radiative neutron capture reaction rate for the \(^{10}\)Be(n,\(\gamma\))\(^{11}\)Be reaction. Comparative analyses are conducted with experimental data, theoretical results from direct radiative capture methods, and transfer reaction calculations. Additionally, we contrast our findings with the existing \(^{10}\)Be(\(\alpha\),\(\gamma\))\(^{14}\)C reaction rate and conclude the dominance of neutron capture over \(\alpha\) capture by \(^{10}\)Be.