The $R$-matrix theory of nuclear scattering is used to consider the meaning of spectroscopic factors for unbound states. Potential scattering is explicitly calculated by constructing an $R$ function which is equivalent to the potential. The compound effects are then parametrized in the usual $R$-matrix fashion with the spectroscopic factors being explicitly included as parameters. The spectroscopic factors are found by fitting data. The spectroscopic factors are very sensitive to the choice of the various resonance parameters, and the validity of spectroscopic factors as a meaningful quantity for unbound states is discussed in the light of several calculations. Several types of resonances found in the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(n,n)\mathrm{}{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(n,n)\mathrm{}{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ are considered. These include the cases of very narrow and very broad resonances and a double-resonance situation.

• Received 29 April 1971

DOI:https://doi.org/10.1103/PhysRevC.4.363