Constraints on theBe7(p,γ)B8radiative capture rate from charge symmetry

Abstract

Cross sections for the dipole radiative capture reactions $^{7}\mathrm{Li}(n,\ensuremath{\gamma})^{8}\mathrm{Li}$ and $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$ are calculated in a two-body model, which is based on a Woods-Saxon parametrization of the nuclear interaction. The well depth is adjusted for each reaction channel so that the measured separation energies and $s$-wave scattering lengths are reproduced. The calculations are repeated for a wide range of the radius and the diffuseness of the interaction. The predicted $S$ factor for the radiative proton capture on $^{7}\mathrm{Be}$ falls within a surprisingly narrow range of values when the model is calibrated to reproduce measurements of the mirror reaction $^{7}\mathrm{Li}(n,\ensuremath{\gamma})^{8}\mathrm{Li}$. The simplified model used here is consistent with the shell model approach for proton capture on $^{7}\mathrm{Be}$ but it gives a significantly smaller cross section for neutron capture on $^{7}\mathrm{Li}$.