Quadrupole and monopole large-amplitude vibrations

A set of nonlinear dynamical equations for quadrupole and monopole moments of nuclei is derived from the time-dependent Hartree-Fock equation by using the so-called moments of the Wigner function. These equations make it possible to describe coupled large-amplitude monopole and quadrupole vibrations. The equations are solved numerically for 208Pb and 40Ca in a model involving separable forces. The giant quadrupole and monopole resonances are reproduced quite well. A distinguishing feature of this large-amplitude motion is the existence of multiphonon states. They are analyzed in detail. Classical and quantum aspects of the analytically solvable one-dimensional purely monopole model are studied to clarify the problem of the anharmonicity of the collective spectrum