Volume conservation in the liquid drop model

Although the L = 0 (breathing) mode does not conserve volume and the L = 2 (quadrupole) mode conserves volume only to first order, both modes together can conserve volume to second order when a certain interference relation among the six mode amplitudes is satisfied. The quantized versions of the liquid drop model with volume conservation imposed to first and to second order have different dynamical groups [IU(5), U(6), respectively], different Hilbert spaces [infinite dimensional, finite dimensional, respectively], and different rotationally invariant operators from which hamiltonians can be constructed. (orig.)