Excitation of low-lying collective states inCa40andPb208by inelastic neutron scattering

Differential cross sections for elastic and inelastic scattering of neutrons from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ targets have been measured at 11, 20, and 25.7 MeV incident energies. The elastic scattering data were used to provide optical model parameters for use in macroscopic and microscopic model analyses of the data using the distorted wave method. The macroscopic model analysis resulted in deformation parameters consistent with those obtained in analogous ($p,p^{\prime }$) reactions which excite the $3^{-}$ and $5^{-}$ collective states in these nuclei. The macroscopic model provides a good description of the differential cross sections. The microscopic model analysis used random-phase approximation detailed wave vectors for the states involved. Two "realistic" effective interactions were studied, one with and one without density dependence. The imaginary contribution to the effective interaction was found to be important in reproducing the shape of the differential cross section in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Exchange amplitudes were calculated exactly. The magnitudes of the $3^{-}$ cross sections for both nuclei were well described by these calculations.