The compound resonances and the bound states observed in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+nucleon system are studied using the continuum shell model. The method of solution involves a division of configuration space as in the $R$-matrix theory. Shell model basis states which are eigenfunctions of the spherical harmonic oscillator potential are employed in the construction of trial wave functions for the internal region. The basis states contain active $1p_{\frac{1}{2}}$, $1d_{\frac{5}{2}}$, and $2s_{\frac{1}{2}}$ orbits as well as higher orbits into which at most a single nucleon is placed. Excitations of up to four particles from the spherical closed core are included. The two-body interaction used in our model was taken from a shell model calculation for ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ by Zuker, supplemented by a two-body central Gaussian interaction from True and a one-body interaction of Woods-Saxon form. Calculated neutron total cross sections, neutron and proton phase shifts as well as differential cross sections and polarizations are presented and compared with experiment. Calculated spectroscopic factors of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ states are also given. The results show excellent qualitative and fair quantitative agreement with experiment. An investigation of the discrepancies between calculated and experimental resonance widths point to our lack of knowledge of the effective interaction.

NUCLEAR STRUCTURE, REACTIONS ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$; calculated bound and continuum eigenstates, $J$, $\pi$, $\Gamma$, $S$. ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(n, n)$, $E<\mathrm{}4\mathrm{}$ MeV, ($p, p$), $E<\mathrm{}6\mathrm{}$ MeV; calculated phase shifts, $\sigma \mathrm{}\left(E\right)\mathrm{}$, $P\left(E\right)\mathrm{}$. Continuum shell model, $R$-matrix discretization.

• Received 1 April 1975

DOI:https://doi.org/10.1103/PhysRevC.12.658