Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.