Isoscalar and Isovector Giant Monopole Vibrations Described by Collective Parameters

Using a recently suggested method, where the nuclear density is parametrized directly, we investigate isoscalar and isovector monopole vibrations. The method is applicable for large amplitude motion, but in this paper it is tested in the simple case of small amplitude vibrations. The parameters are a radial scaling parameter and a surface skin-thickness parameter for each of the neutron and proton density distributions. The energy of the isoscalar (isovector) mode as function of nucleon number is obtained with an accuracy of 4% (15%) for different forces. The isoscalar state is for nuclei above 40 Ca an overall scaling vibration. The isovector state for the same nuclei is mainly a scaling mode, but it contains significant contributions from the diffuseness degrees of freedom. The masses related to the two modes are found to be nearly equal. They vary from light to heavy nuclei from 100% to 60% of the total nuclear mass. The technical and physical advantages of the method are strikingly demonstrated by this successful application.