A simple microscopic approach to the nuclear giant monopole and quadrupole resonances

The monopole and quadrupole excitation modes of spin-saturated nuclei are studied by means of sum rules, using a simple density-dependent finite-range interaction with particular emphasis on the effects of the finite range of the interaction on the excitation energies. Within the framework of the density matrix expansion, it is shown that the excitation energies can be related to the various contributions coming from the total energy of a nucleus. This approach has the advantage of separating out a part from the relations of the excitation energies which exists only for a finite-range interaction and vanishes for zero-range interactions of the Skyrme type. (author)