Elastic and Inelastic Proton Scattering from Even Isotopes of Cd, Sn, and Te

Protons of 16-MeV energy were scattered from isotopically enriched targets of ${}_{}{}^{110,112,114,116}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{112,116,118,120,122,124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{126,128,130}{}_{}{}^{}\mathrm{Te}$. Differential cross sections were measured for scattering to the $0^{+}$ ground state and the first $2^{+}$ and $3^{-}$ collective states. As the mass number $A$ increases, the elastic angular distributions shift towards smaller angles and show increasing damping. The $2^{+}$ and $3^{-}$ cross sections show a systematic decrease in magnitude with increasing $A$. Optical-model calculations were made by fixing the geometrical parameters for each set of isotopes and searching on $V$ and $W_D$, the real and surface imaginary parts of the optical potential. The observed trends, systematically increasing with $A$, are consistent with an isospin dependence in the real and imaginary parts of the optical potential. The distorted-wave program dwuck, assuming a collective vibrational model, was run using complex coupling and Coulomb excitation in order to extract deformation parameters ${\beta }_l$ for all the $2^{+}$ and $3^{-}$ states. These parameters indicate that the decrease in inelastic scattering with increasing $A$ is associated with a decreasing collectivity for each set of isotopes. The values of ${\beta }_l$ are in reasonable agreement with deformation parameters extracted by other methods.