Alpha-transfer reactions in light nuclei. III. (Li7,t) stripping reaction

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reactions have been studied at a beam energy of 38 MeV. At this energy these reactions exhibit a high selectivity for populating α-particle cluster states. The angular distributions for these states have been analyzed using an exact-finite-range coupled-channels Born-approximation code incorporating final-state cluster wave functions derived from an α-core folded potential. The resulting $\alpha$-particle spectroscopic factors ($S_{\alpha }$) for the $0^{+}$, $2^{+}$, and $4^{+}$ members of the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ground state band are in good agreement with cluster model predictions. For the 7.12-MeV ($1^{-}$) state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, the spectroscopic factor ($S_{\alpha }\approx 0.20$) is consistent with other analyses but is uncertain by a factor of 2 due to the presence of significant compound-nuclear contributions to this transition. In general, for those states which are not selectively populated at forward angles the measured angular distributions are well described by a Hauser-Feshbach calculation. In particular it is shown that both the magnitude and shape of the angular distributions for the 11.10-MeV ($4^{+}$) state populated in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reactions can be well accounted for in terms of statistical compound-nuclear contributions. The elastic scattering of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ions from several light targets has also been studied and optical-model potentials derived.