QUADRUPOLE AND MONOPOLE LARGE-AMPLITUDE VIBRATIONS

A set of nonlinear dynamical equations for quadrupole and monopole mom ents of nuclei is derived from the time-dependent Hartree-Fock equatio n by using the so-called moments of the Wigner function. These equatio ns make it possible to describe coupled large-amplitude monopole and q uadrupole vibrations. The equations are solved numerically for Pb-208 and Ca-40 in a model involving separable farces. The giant quadrupole and monopole resonances are reproduced quite well. A distinguishing fe ature of this large-amplitude motion is the existence of multiphonon s tates. They are analyzed in detail. Classical and quantum aspects of t he analytically solvable one-dimensional purely monopole model are stu died to clarify the problem of the anharmonicity of the collective spe ctrum.