Based on an extended Skyrme interaction that includes the terms in relative momenta up to sixth order, corresponding to the so-called Skyrme pseudopotential up to next-to-next-to-next-to leading order (N3LO), we derive the expressions of Hamiltonian density and single nucleon potential under general non-equilibrium conditions which can be applied in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei. While the conventional Skyrme interactions, which include the terms in relative momenta up to second order, predict an incorrect behavior as a function of energy for nucleon optical potential in nuclear matter, the present extended N3LO Skyrme interaction can give a nice description for the empirical nucleon optical potential. We also construct three interaction sets with different high-density behaviors of the symmetry energy, by fitting both the empirical nucleon optical potential up to energy of 1 GeV and the empirical properties of isospin asymmetric nuclear matter. These extended N3LO Skyrme interactions will be useful in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei at intermediate and high energies, and they can also be useful in nuclear structure studies within the mean-field model.

Exploring nucleon drip lines and astrophysical rapid neutron capture process (r-process) paths in the nuclear landscape is extremely challenging in nuclear physics and astrophysics. While various models predict similar proton drip line, their predictions for neutron drip line and the r-process paths involving heavy neutron-rich nuclei exhibit a significant variation which hampers our accurate understanding of the r-process nucleosynthesis mechanism. Using microscopic density functional theory with a representative set of non-relativistic and relativistic interactions, we demonstrate for the first time that this variation is mainly due to the uncertainty of nuclear matter symmetry energy Esym(ρsc) at the subsaturation cross density ρsc = 0.11/0.16 × ρ0 (ρ0 is saturation density), which reflects the symmetry energy of heavy nuclei. Using the recent accurate constraint on Esym(ρsc) from the binding energy difference of heavy isotope pairs, we obtain quite precise predictions for the location of the neutron drip line, the r-process paths and the number of bound nuclei in the nuclear landscape. Our results have important implications on extrapolating the properties of unknown neutron-rich rare isotopes from the data on known nuclei. 1. Introduction.-The determination of the location of neutron and proton drip lines in the nuclear landscape is a fundamental question in nuclear physics. The drip lines tell us what is the limit of the nuclear stability against nucleon emission and how many bound nuclei can exist in the nuclear chart [1]. The quest for the neutron drip line (nDL) is also important for understanding the astrophysical rapid neutron capture process (r-process) which occurs along a path very close to the nDL in the nuclear landscape and provides a nucleosynthesis mechanism for the origin of more than half of the heavy nuclei in the Universe [2][3][4][5]. While the proton drip line (pDL) has been determined up to Protactinium (proton number Z = 91) [6], there has little experimental information on the nDL for Z > 8 [7]. Since the majority of rare isotopes inhabiting along the nDL and the r-process paths are unlikely to be observed in the terrestrial laboratory, their information has to rely on the model extrapolation based on the known nuclei, which is so far largely uncertain and hampers our accurate understanding of the r-process nucleosynthesis mechanism [8][9][10][11]. To understand and reduce the uncertainty of the model extrapolation from the known nuclei to the unknown neutron-rich rare isotopes is thus of critical importance, and we show here the symmetry energy plays a key role in this issue.

We develop a new lattice Hamiltonian method for solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to treat the collision term and using the GPU parallel computing to carry out the calculations allows for a rather high accuracy in evaluating the collision term, especially its Pauli blocking, leading thus to a new level of precision in solving the BUU equation. Applying this lattice BUU method to study the width of giant dipole resonance (GDR) in nuclei, where the accurate treatment of the collision term is crucial, we find that the obtained GDR width of 208 Pb shows a strong dependence on the in-medium nucleon-nucleon cross section σ * NN. A very large medium reduction of σ * NN is needed to reproduce the measured value of the GDR width of 208 Pb at the Research Center for Nuclear Physics in Osaka, Japan.