A selection rule for fragmentations of doorway $s$-hole states in light nuclei is given. In the two-body fragmentation process of the doorway $s$-hole states in light nuclei, smaller fragments than the $\alpha$ particle ($p$, $n$, $d$, $t$, and 3He) are allowed, while the fragments such as the $\alpha$ particle and the larger particles are forbidden, in spite of the fact that the $Q$ value for the $\alpha$ fragment is similar to or even larger than those for the $p$, $n$, and $d$ fragments. The selection rule comes from the spatial symmetry of the doorway $s$-hole states. The spectroscopic factors and partial widths for the two-body fragmentations of the $s$-hole state of ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ are calculated to show the selection rule. The calculated escape widths for the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}(s-\mathrm{hole})$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(s-\mathrm{hole})$ doorway states are in good correspondence with the experimental widths. This may suggest that the following scenario is realized; in light nuclei the fragmentation process of the $s$-hole state in the doorway stage is superior or competitive to that in the compound nuclear stage.

• Received 16 October 1995

DOI:https://doi.org/10.1103/PhysRevC.53.752