Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinate and collective momentum, we microscopically derive the collective Hamiltonian for low-frequency quadrupole modes of excitation. We
show that the five-dimensional collective Schrodinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We focus on basic ideas and recent advances of the approaches based on the time-dependent mean-field theory, but relations to other time-independent approaches are also briefly discussed.
We demonstrate the damping of quantum octupole vibrations near the touching point when two colliding nuclei approach each other in the mass-asymmetric $^{208}$Pb + $^{16}$O system, for which the strong fusion hindrance was clearly observed. We, for t
he first time, apply the random-phase approximation method to the heavy-mass asymmetric di-nuclear system to calculate the transition strength $B$(E3) as a function of the center-of-mass distance. The obtained $B$(E3) strengths are substantially damped near the touching point, because the single-particle wave functions of the two nuclei strongly mix with each other and a neck is formed. The energy-weighted sums of $B$(E3) are also strongly correlated with the damping factor which is phenomenologically introduced in the standard coupled-channel calculations to reproduce the fusion hindrance. This strongly indicates that the damping of the quantum vibrations universally occurs in the deep sub-barrier fusion reactions.
We demonstrate that when two colliding nuclei approach each other, their quantum vibrations are damped near the touching point. We show that this damping is responsible for the fusion hindrance phenomena measured in the deep sub-barrier fusion reacti
ons. To show those, we for the first time apply the random-phase-approximation (RPA) method to the two-body $^{16}$O + $^{16}$O and $^{40}$Ca + $^{40}$Ca systems. We calculate the octupole transition strengths for the two nuclei adiabatically approaching each other. The calculated transition strength drastically decreases near the touching point, strongly suggesting the vanishing of the quantum couplings between the relative motion and the vibrational intrinsic degrees of freedom of each nucleus. Based on this picture, we also calculate the fusion cross section for the $^{40}$Ca + $^{40}$Ca system using the coupled-channel method with the damping factor simulating the vanishing of the couplings. The calculated results reproduce well the experimental data, indicating that the smooth transition from the sudden to adiabatic processes indeed occurs in the deep sub-barrier fusion reactions.
On the basis of time-dependent mean-field picture, we discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes as representatives of surface shape vibrations of a superfluid droplet (nucleus). We c
onsider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. We show that the intimate connections between the BCS pairing and collective vibrations reveal through the inertial masses governing their collective kinetic energies.
