Nuclear collective dynamics in the lattice Hamiltonian Vlasov method

The lattice Hamiltonian method is developed for solving the Vlasov equation with nuclear mean-field based on the Skyrme pseudopotential up to next-to-next-to-next-to leading order. The ground states of nuclei are obtained through varying the total energy with respect to the density distribution of nucleons. Owing to the self-consistent treatment of initial nuclear ground state and the exact energy conservation in the lattice Hamiltonian method, the present framework of solving the Vlasov equation exhibits very stable nuclear ground state evolution. As a first application of the new lattice Hamiltonian Vlasov method, we explore the iso-scalar giant monopole and iso-vector giant dipole modes of finite nuclei. The obtained results are shown to be comparable to that from random-phase approximation and consistent with the experimental data, indicating the capability of the present method in dealing with the long-time near-equilibrium nuclear dynamics.