{sup 15}C-{sup 15}F Charge Symmetry and the {sup 14}C(n,{gamma}){sup 15}C Reaction Puzzle

The low-energy reaction {sup 14}C(n,{gamma}){sup 15}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 {sup 14}C(n,{gamma}){sup 15}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 {sup 15}C{yields}{sup 14}C+n and the real {sup 15}F{yields}{sup 14}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 {sup 15}C and {sup 15}F mirror pair. This brings into question the experimental determinations of the astrophysically important (n,{gamma}) cross sections for short-lived radioactive targets.