Isospin and macroscopic models for the excitation of giant resonances and other collective states

Abstract

Recently there has been some confusion over the excitation of “isovector” giant resonances by isoscalar probes. We present a unified theoretical description of macroscopic models that may be used to calculate the excitation of giant resonances by inelastic scattering so as to clarify this and related questions. Particular attention is given to the relative phase of the Coulombic and hadronic contributions. After describing models for the transition densities that are based upon certain sum rules, a folding model and a deformed optical potential model for the transition potentials are discussed. Applications are made to some examples of inelastic α-particle scattering and the two models are compared. Folding yields cross sections for the breathing-mode monopole resonance that are smaller than those from the potential model by almost a factor of two, so that the measured values appear to require more than 100% depletion of the sum rule. It is suggested that this might be due to neglect of density dependence in the effective interaction.