Multiphonon states in a solvable model Original Research Article

A set of non-linear dynamical equations for monopole and quadrupole moments of nuclei is derived from the TDHF equation using the Wigner function moments. It provides a description of coupled large amplitude monopole and quadrupole vibrations. The equations are solved numerically in the model of the harmonic oscillator with Q-Q residual interaction. The Fourier analysis exhibits giant quadrupole and monopole resonances and multiphonon states built on them. The problem of the quantization of the classical collective motion is studied. The quantization of the model allows one to observe the spectrumʹs anharmonicity that falls with nuclear mass A as ∼ A−2. The collective Hamiltonian is constructed. It turns out that its potential energy surface has a finite barrier height with respect to quadrupole motion.