A multilevel two-channel $R$-matrix analysis is made for both the neutron total and angle-integrated ($n,\alpha$) cross sections of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ for 0-5.8-MeV neutrons. Off-resonant phase shifts are described by scattering in a real Woods-Saxon local potential with a spin-orbit term and a parity dependence for the well depths. The well parameters are chosen to bind the $1d_{\frac{5}{2}}$ and $2s_{\frac{1}{2}}$ levels at the energies of the lowest two states in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ and the quasibound $1d_{\frac{3}{2}}$ level at the centroid of five observed ${\frac{3}{2}}^{+}$ resonances. The $1d_{\frac{3}{2}}$ level is replaced by these five fragments which contain nearly 100% of the $1d_{\frac{3}{2}}$ strength and have their eigenenergy centroid at 5.74 MeV in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$. The 5.08-MeV level in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ has 69% of the strength. The $R$-matrix boundary radius must be chosen carefully inside the tail of the potential in order to subtract the $1d_{\frac{3}{2}}$ state and in order to place the unbound $2p$ and $1f$ states at energies consistent with the observed $p$-and $f$-wave fragments. Spectroscopic factors are deduced for 26 levels in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ between 4.5 and 9.5 MeV and the sums of these factors are 1% for $J^{\pi }={\frac{1}{2}}^{+}$; 5% for ${\frac{1}{2}}^{-}$; 12% for ${\frac{3}{2}}^{-}$; 99% for ${\frac{3}{2}}^{+}$; 0.1% for ${\frac{5}{2}}^{+}$; 1% for ${\frac{5}{2}}^{-}$; and 14% for ${\frac{7}{2}}^{-}$. Thus, the observed single-particle structure of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ in both the bound and unbound region is described by an $R$-matrix-plus-potential analysis.

• Received 15 August 1972

DOI:https://doi.org/10.1103/PhysRevC.7.561