Intermediate-State Theory of Single-Particle Resonances

The $d_{\frac{3}{2}}$ state in oxygen is observed as a very sharp scattering resonance in ${\mathrm{O}}^{16}\mathrm{}(n,n)\mathrm{}{\mathrm{O}}^{16}$. The state is a "virtual" state, therefore, and its inclusion among the single-particle discrete states employed in the shell-model description of states of ${\mathrm{O}}^{16}$ requires some justification. In this paper a unified reaction theory recently given by one of the authors is used as the basis of a description in which the resonance is described as arising from the virtual transitions into a true bound state. The continuum states of this description are nonresonant because the continuum $d_{\frac{3}{2}}$ resonance is replaced by a bound $d_{\frac{3}{2}}$ state which plays the role of a new "doorway state." This description leads to the conventional shell-model description of the particle-hole resonances of ${\mathrm{O}}^{16}$ and simplifies the description of the interaction between virtual and bound states.