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 isoscalar giant monopole and isovector giant dipole modes of finite nuclei. The obtained results are shown to be comparable to that from random-phase approximation and are consistent with the experimental data, indicating the capability of the present method in dealing with the long-time near-equilibrium nuclear dynamics.

Figure 1

The time evolution of radial density profile of ground state ${}^{208}\mathrm{Pb}$ based on the present LHV method, with $\mathrm{N}3\mathrm{LO}$ Skyrme pseudopotential $\mathrm{SP}6\mathrm{m}$ up to $200\mathrm{fm}/c$.

Figure 2

Same as Fig. 1 but up to 1000 $\mathrm{fm}/c$.

Figure 3

Time evolution of (a) rms radius, (b) the fraction of bound nucleons, and (c) binding energy of ground state ${}^{208}\mathrm{Pb}$ with $\mathrm{N}3\mathrm{LO}$ Skyrme pseudopotential $\mathrm{SP}6\mathrm{m}$ up to $1000\mathrm{fm}/c$. Calculations are performed with time step $\mathrm{\Delta }t=0.4\mathrm{fm}/c$, and $N_{\mathrm{E}}=5000$ and $10000$, respectively.

Figure 4

The time evolution of $\mathrm{\Delta }{\langle \widehat{Q}\rangle }_{\mathrm{ISM}}$ of ${}^{208}\mathrm{Pb}$ after a perturbation of ${\widehat{H}}_{ex}\left(t\right)=\lambda {\widehat{Q}}_{\mathrm{ISM}}\delta \left(t\right)$ with $\lambda =100\mathrm{MeV}{\mathrm{fm}}^{-1}/c$. The results correspond to three $\mathrm{N}3\mathrm{LO}$ Skyrme pseudopotentials, $\mathrm{SP}6\mathrm{s}, \mathrm{SP}6\mathrm{m}, \mathrm{SP}6\mathrm{h}$, and one conventional Skyrme interaction $\mathrm{MSL}1$, respectively.

Figure 5

Strength function of isoscalar monopole mode calculated based on the LHV method with $\mathrm{SP}6\mathrm{s}, \mathrm{SP}6\mathrm{m}, \mathrm{SP}6\mathrm{h}$, and $\mathrm{MSL}1$. The experimental peak energy and that from RPA calculation with MSL1 are also included for comparison.

Figure 6

Same as Fig. 4 but for isovector dipole mode.

Figure 7

Same as Fig. 5 but for isovector dipole mode.