Nuclear Sum Rules, Electron Scattering and Giant Resonances

The isoscalar sum rules of Deal and Fallieros (1973) and generalizations of these sum rules are discussed. The isoscalar form factor and transition density for an arbitrary eigenstate of the nucleus are given as sums over the sum rules and, for a particular choice of the operators in the sum rules, are given by a series of which the first terms are the same as the results of the hydrodynamical model. It is shown that caution is needed in making nuclear spin assignments from inelastic electron scattering. The sum rule of Deal and Fallieros is used to clarify the calculation of Bohr and Mottelson (1975) of the energy of the isosca1.ar giant quadrupole resonance.