Excitation of ${}^{208}\mathrm{Pb}$ in light ion induced reactions and the two octupole phonon multiplet

To identify the states of the $0^{+},$ $2^{+},$ $4^{+},$ and $6^{+}$ two octupole phonon (TOP) multiplet in ${}^{208}\mathrm{Pb}$ and their respective fragmentation inelastic proton, deuteron, and $\alpha$ scattering has been measured in high energy resolution. Quantum numbers and spectroscopic factors of excited states up to 8 MeV are obtained from the ${}^{207}\mathrm{Pb}{\mathrm{}(d,p)\mathrm{}}^{208}\mathrm{Pb}$ transfer reaction with vector polarized deuterons. From the comparison with literature, we conclude that up to $E_x=6\mathrm{}$ MeV, essentially all states are resolved. The data are compared with recent calculations within the quasiparticle phonon model. For the lowest states the calculated energies are in excellent agreement with experiment. The calculated spectrum of $0^{+},$ $2^{+},$ $4^{+},$ and $6^{+}$ states, which includes mixing with the TOP multiplet, is related to experimental states up to excitation energies above twice the excitation energy of the collective $3_1^{-}$ state at $E_x=5230\mathrm{}$ keV. The measured excitation strengths are consistent with the predicted fragmentation of the two octupole phonon states.