  The information on pygmy resonances reveals new aspects on the isospin
dynamics of the nucleus with important astrophysical consequences. In this
connection, the precise knowledge of nuclear response functions plays a key
role in the determination of photonuclear reactions cross sections which are of
importance for the synthesis of heavy neutron-rich elements. For that purpose,
a theoretical method based on density functional theory and multi-phonon
approach is applied for investigations of nuclear excitations with different
multipolarities and energies in stable and exotic nuclei. The possible relation
of low-energy modes to the properties of neutron or proton skins is
systematically investigated for isotonic and isotopic chains. Our studies of
dipole and quadrupole response functions and the corresponding transition
densities indicate new pygmy dipole and pygmy quadrupole resonances, describing
oscillations of the nuclear skin. Also, the presence of skins is found to
affect the magnetic response of nuclei.
