# Nuclear collective dynamics in the lattice Hamiltonian Vlasov method

## TL;DR

This paper introduces a new lattice Hamiltonian method for solving the Vlasov equation in nuclear physics, enabling stable simulation of nuclear ground states and collective excitations with results consistent with experiments.

## Contribution

The paper develops a novel lattice Hamiltonian Vlasov approach incorporating Skyrme pseudopotential up to N3LO, improving stability and accuracy in nuclear dynamic simulations.

## Key findings

- Stable nuclear ground state evolution demonstrated.
- Results for giant monopole and dipole modes agree with RPA and experiments.
- Method effectively models long-time nuclear dynamics.

## Abstract

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.