Giant multipole resonances from inelastic scattering of 152-MeV alpha particles

Abstract

Giant resonance spectra have been measured for $^{208}\mathrm{Pb}$, $^{120}\mathrm{Sn}$, $^{90}\mathrm{Zr}$, $^{58}\mathrm{Ni}$, and $^{46}\mathrm{Ti}$, using inelastic scattering of 152-MeV alpha particles. In addition to some low-lying states, the spectra were analyzed to yield separate peaks for the giant quadrupole resonance and giant monopole resonance, except in $^{46}\mathrm{Ti}$, where no evidence was found for a giant monopole resonance. The results for the monopole resonance when compared to distorted-wave Born-approximation calculations show that \ensuremath{\sim}100% (\ifmmode\pm\else\textpm\fi{}20%) of the $T=0$, $L=0$ energy weighted sum rule is depleted for nuclei with $A>90$. For $^{58}\mathrm{Ni}$ only 40% of the monopole sum rule is found. The excitation energy of the giant monopole resonance follows the systematic trend $\ensuremath{\sim}80{A}^{\ensuremath{-}\frac{1}{3}}$ MeV. The data are also compared with folding model calculations using Tassie transition densities and an effective interaction derived from elastic data. Good agreement was obtained for low-lying quadrupole and octopole excitations, but this model yields considerably too little cross section for the monopole resonance. This probably indicates a deficiency in the Tassie model breathing mode transition density.NUCLEAR REACTIONS $^{208}\mathrm{Pb}$, $^{120}\mathrm{Sn}$, $^{90}\mathrm{Zr}$, $^{58}\mathrm{Ni}$, $^{46}\mathrm{Ti}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=152$ MeV, ${E}_{\ensuremath{\chi}}=0\ensuremath{-}40$ MeV; measured $\ensuremath{\sigma}({E}_{\ensuremath{\chi}}, \ensuremath{\theta})$; discuss giant resonances, folding model calculations, deduced $L$, ${\ensuremath{\beta}}_{L}$.