Nuclear Spreading Widths of Particle-Vibration½+Doorway Resonances inPb207andPb209

The nuclear spreading widths of the ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ ${\mathrm{½}}^{+}$ doorway resonances are calculated in a particle-vibration model. The hallway states are of the particle—two-photon type. The fine structure in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ is essentially due to the availability of many hallways (some with large matrix elements) and their proximity to the doorway. The ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ ${\mathrm{½}}^{+}$ doorway spreading widths are found to be in line with the experimental situation.