Isobaric-Spin Impurities ofF18States fromN14(α, n)F17(0.500)N14(α, p)O17(0.871)Cross-Section Ratios

A pair of mirror reactions initiated with $\alpha$ particles was chosen to estimate the isobaric-spin impurity of the intermediate compound-nuclear states in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$. Total-cross-section ratios of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\alpha , n){}_{}{}^{17}{}_{}{}^{}\mathrm{F}\mathrm{}\left(0.500\right)\mathrm{}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\alpha , p){}_{}{}^{17}{}_{}{}^{}\mathrm{O}\mathrm{}\left(0.871\right)\mathrm{}$ mirror reactions were measured in 100-keV steps from $E_{\alpha }=7\mathrm{} \mathrm{to} 12$ MeV by recording the isotropic deexcitation $\gamma$ rays from the ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$(0.500), ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$(0.871), and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$(3.058) states. Considerable structure indicative of compound-nucleus formation was observed in the ratios plotted against $\alpha$ energy, with major maxima at $E_{\alpha }=8.12, 9.5, 10.07, \mathrm{and} 11.52$ MeV. Symmetric angular distributions at three of these maxima resulted in tentative spin assignments of ($2^{-}$) at a ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ excitation of 10.764±0.030 MeV, ($2^{-}$, $3^{-}$, $3^{+}$) at 12.234±0.030 MeV, and ($2^{-}$, $3^{+}$) at 13.361±0.030 MeV. These states are unambiguously $T=0\mathrm{}$, in contrast with the forbidden-reaction isobaric-spin assignments, having estimated $T=1\mathrm{}$ impurities of 12%, 3-12%, and 2-3%, respectively. A comparison is made with earlier isobaric-spin-impurity measurements that utilized forbidden reactions, and the agreement is good after those forbidden-reaction estimates incorporating a statistical theory of the compound nucleus are reduced by a factor of $\frac{3}{2}$. This correction arises from the forbidden reactions proceeding through both impure $T=0\mathrm{}$ and impure $T=1\mathrm{}$ states, which are of comparable density in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$.