Double-Octupole States in ${}_{}{}^{208}{}_{}{}^{}Pb$

The states of ${}^{208}\mathrm{Pb}$ are calculated in a 24 orbit model space which includes all excitations up to two particles and two holes beyond the closed shell. All of the known low-lying states are reproduced by this model. The observed distributions of electromagnetic excitation strength from the ground state to low-lying excited states are well described by the model. The double-octupole excitation strength is calculated and found to be concentrated in $0^{+}$, $2^{+}$, and $4^{+}$ states around 5.2 MeV, but it is fragmented over many $6^{+}$ states, in agreement with recent experiments.