Collective potentials and dipole and quadrupole giant resonances

The dynamic collective model is extended into the energy region immediately above the giant dipole resonances, i.e. into an energy region between 20 and 28 MeV. The total Hamiltonian is constructed and the dynamical problem is solved by diagonalizing the Hamiltonian in the basis of a five-dimensional harmonic oscillator. In schematical studies the splitting of giant quadrupole resonances is shown. For some elements the potential energy surfaces (PES) are constructed within the collective model developed by Gneuss et al. and the quadrupole resonances have been calculated in the framework of the dynamic collective model. In the last part the agreement with experimental data is shown. (Auth.)