The low-energy reaction ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ provides a rare opportunity to test indirect methods for the determination of neutron capture cross sections by radioactive isotopes versus direct measurements. It is also important for various astrophysical scenarios. Currently, puzzling disagreements exist between the ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ cross sections measured directly, determined indirectly, and calculated theoretically. To solve this puzzle, we offer a strong test based on a novel idea that the amplitudes for the virtual ${}^{15}\mathrm{C}\to {}^{14}\mathrm{C}+n$ and the real ${}^{15}\mathrm{F}\to {}^{14}\mathrm{O}+p$ decays are related. Our study of this relation, performed in a microscopic model, shows that existing direct and some indirect measurements strongly contradict charge symmetry in the ${}^{15}\mathrm{C}$ and ${}^{15}\mathrm{F}$ mirror pair. This brings into question the experimental determinations of the astrophysically important ($n,\gamma$) cross sections for short-lived radioactive targets.

• Received 8 November 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.162501