High-$j$ neutron excitations outside ${}^{136}$Xe

The $\nu 0h_{9\mathrm{/}2}$ and $\nu 0i_{13\mathrm{/}2}$ strength at ${}^{137}$Xe, a single neutron outside the $N=82$ shell closure, has been determined using the ${}^{136}$Xe($\alpha$,${}^3$He)${}^{137}$Xe reaction carried out at 100 MeV. We confirm the recent observation of the second 13/2${}^{+}$ state and reassess previous data on the 9/2${}^{-}$ states, obtaining spectroscopic factors. These new data provide additional constraints on predictions of the same single-neutron excitations at ${}^{133}$Sn.