Energies and moments of giant resonances for isoscalar monopole and quadrupole excitations: A sum-rule approach

An approach to isoscalar giant resonances in terms of their energy moments is proposed. Besides the well-known moment containing the energy to power plus one, moments with powers plus three and minus one are evaluated. Values for the giant resonance energy and a limit on its width are obtained. The approach systematises and unifies various collective theories, and gives a simple derivation of the quadrupole energy as √2 times the oscillator quantum.