Single-nucleon transfer to unbound states in the ${}^4\mathrm{He}(\alpha {,t)}^5\mathrm{Li}$ reaction at incident energies of 120, 160, and 200 MeV

The ${}^4\mathrm{He}\left(\alpha {,t)}^5\mathrm{Li}\right(\mathrm{g}.\mathrm{s}.\mathrm{})\mathrm{}$ reaction was investigated at incident energies of 120, 160, and 200 MeV in order to resolve discrepancies found between previous measurements and theoretical predictions for the analogous reaction ${}^4{\mathrm{H}\mathrm{e}(\mathrm{\alpha },}^3{\mathrm{H}\mathrm{e})}^5\mathrm{He}(\mathrm{g}.\mathrm{s}.\mathrm{})\mathrm{}$ at these energies. The line shapes of the ${}^5\mathrm{Li}$ ground-state resonance in the measured triton energy spectra are well reproduced by distorted-wave Born approximation (DWBA) calculations. Cluster-core optical potentials, which yield better overall agreement both for $\alpha -\alpha$ elastic scattering and for the single-nucleon transfer reactions, are presented. It is shown that the previously observed discrepancies in magnitude between measured and calculated cross sections by a factor of $\sim 2$ can be improved by employing spectroscopic factors obtained from a realistic shell model for the transitions to the final mass-3 and mass-5 systems.