Characteristics of the Differential Cross Sections for the Low-Energy (p, n) Reaction on the Spin-½ Medium-Mass Nuclei

The differential cross sections of neutron groups resulting from the bombardment of isotopically enriched ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{113}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{117}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ targets with a 5.35-MeV pulsed proton beam have been measured with a time-of-flight system. The observed angular distributions $\sigma \left(\theta \right)$ of the neutron groups feeding the low-lying residual states are all consistent with symmetry about $\theta =90\mathrm{}°$. They show the following distinct features which characterize the spin change $\Delta I=I_f-I_i$, where $I_i$ and $I_f$ are the spin values of the target and residual states: $\Delta I=0\mathrm{}$ transitions exhibit pronounced forward angle peaking; $\Delta I=1\mathrm{}$ transitions are isotropic; $\Delta I=2\mathrm{}$ transitions show mild peaking around 90°; the integrated differential cross section for $\Delta I=1\mathrm{}$ is greater than that for $\Delta I=0\mathrm{}$ for transitions from a given target nucleus leading to residual states with similar energies. A simplified consideration of the conservation of angular momentum and parity in the framework of the statistical theory of compound-nuclear reactions reveals that the characteristic shape of $\sigma \left(\theta \right)$ associated with the $\Delta I$ of a transition is a manifestation of the conservation laws. The experimental results also compare reasonably well with the theoretical predictions of the generalized Hauser-Feshbach theory of nuclear reactions.