Nuclear Response Function

A fast numerical method is described for calculating nuclear excitation properties with $\delta$-type interactions. The method is applied to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, and the following properties of the nucleus are found: (i) The quadrupole strength has two main pieces, one a low state and one identifiable as the giant quadrupole; (ii) excitations with $L>\mathrm{}2\mathrm{}$ do not seem to have high-energy collective parts; (iii) the giant dipole $L=1\mathrm{}$, $T=1\mathrm{}$ is too low unless the interaction has a strong momentum dependence.