Giant monopole and quadrupole resonances and other multipole excitations inPb208studied in 43 MeV/nucleonα-particle and deuteron scattering

Inelastic excitations of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ up to the giant resonance region were investigated in 172 MeV $\alpha$ and 86 MeV $d$ scattering. In the spectra, the giant resonance bump exhibits a double structure; the well known isoscalar giant quadrupole resonance at 10.9 ± 0.3 MeV, and the new resonance at 13.8 ± 0.3 MeV, for which evidence exists for $L=0\mathrm{}$. Both resonances have a full width at half maximum of 2.6 ± 0.3 MeV. Below the giant resonances two new structures were found at excitation energies of 7.4 and 8.1 MeV which were identified as hexadecapole excitations with a strength of 3 and 2.7 single particle units, respectively. Angular distributions have been obtained for highlying excitations as well as for the low-lying $3^{-}$, $5^{-}$, $2^{+}$, and $4^{+}$ states. Microscopic distorted-wave Born-approximation calculations have been performed using double folding form factors. In this approach a good description of our scattering data has been achieved. For low-lying excitations our results are consistent with electron and proton scattering analyses. For the giant quadrupole resonance the angular distributions cannot be described assuming pure $L=2\mathrm{}$ excitation. Different assumptions about other contributing multipole strengths are discussed. Assuming the 13.8 MeV resonance to be the giant monopole excitation, several models yield differential cross sections which are inconsistent with the data. A consistent description of $\alpha$ and $d$ scattering is obtained if, in addition to the compressional $L=0\mathrm{}$ mode, diffuseness effects are considered as well as other contributing multipole strength ($L=1\mathrm{}$). With the transition density used, the monopole strength corresponds to about 90% of the energy weighted sum rule limit. The result of a recent ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering experiment suggesting a pronounced $L=3\mathrm{} \mathrm{and} 5$ resonance at $E_x\simeq 20$ MeV in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ is not confirmed.