Double-Magic Nature ofSn132andPb208through Lifetime and Cross-Section Measurements

Single-neutron states in $^{133}\mathrm{Sn}$ and $^{209}\mathrm{Pb}$, which are analogous to single-electron states outside of closed atomic shells in alkali metals, were populated by the ($^{9}\mathrm{Be}$, $^{8}\mathrm{Be}$) one-neutron transfer reaction in inverse kinematics using particle-$\ensuremath{\gamma}$ coincidence spectroscopy. In addition, the ${s}_{1/2}$ single-neutron hole-state candidate in $^{131}\mathrm{Sn}$ was populated by ($^{9}\mathrm{Be}$, $^{10}\mathrm{Be}$). Doubly closed-shell $^{132}\mathrm{Sn}$ (radioactive) and $^{208}\mathrm{Pb}$ (stable) beams were used at sub-Coulomb barrier energies of 3 MeV per nucleon. Level energies, $\ensuremath{\gamma}$-ray transitions, absolute cross sections, spectroscopic factors, asymptotic normalization coefficients, and excited-state lifetimes are reported and compared with shell-model expectations. The results include a new transition and precise level energy for the $3{p}_{1/2}$ candidate in $^{133}\mathrm{Sn}$, new absolute cross sections for the $1{h}_{9/2}$ candidate in $^{133}\mathrm{Sn}$ and $3{s}_{1/2}$ candidate in $^{131}\mathrm{Sn}$, and new lifetimes for excited states in $^{133}\mathrm{Sn}$ and $^{209}\mathrm{Pb}$. This is the first report on excited-state lifetimes of $^{133}\mathrm{Sn}$, which allow for a unique test of the nuclear shell model and $^{132}\mathrm{Sn}$ double-shell closure.