Mixing of Two-Particle, Two-Hole States inPb208

The two-neutron transfer reactions ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}(t, p){}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{210}{}_{}{}^{}\mathrm{Pb}(p, t){}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been employed to study states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Several strongly excited states up to 6-MeV excitation can be described as two-particle, two-hole states with strong correlations between the two particles and separately between the two holes. The cross sections to such two-particle, two-hole states are found to be in qualitative agreement with those observed for the $2^{+}$ states in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{210}{}_{}{}^{}\mathrm{Pb}$ in the ($p, t$) and ($t, p$) reactions, respectively. A state with $J^{\pi }=0^{+}$ near 5.2-MeV excitation in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ is discussed in terms of a two-octupole phonon wave function.