${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(t,d)\mathrm{}{}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ Reaction with 20-MeV Tritons

Spectroscopic factors for the single-neutron states in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ have been determined from angular distributions of the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(t,d)\mathrm{}{}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ reaction. The 1.42-MeV level was found to contain only part of the $j_{\frac{15}{2}}$ single-particle strength. A neutron-bound-state well which reproduces the observed level order and spacings of the positive-parity single-particle states and also gives shell-model-like spectroscopic factors is discussed. Both counter-telescope and magnetic-spectrograph techniques were employed, the latter method being used to extend the spectrum to higher excitation energies. A number of previously unreported levels in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ are noted. Elastic-scattering measurements were also carried out and the resulting optical-model analysis used in distorted-wave calculations. These calculations indicate that the ($t,d$) reaction is insensitive to cutoff radii and to the choice of either of two sets of triton optical-model potentials which fit the elastic-scattering data.