Isospin Effects On Ground State And Dynamical Properties Of Finite Nuclei

The isospin effects on ground state and dynamical properties of finite nuclei reflects the isospin dependence of in-medium nuclear effective interaction,while the isospin dependence of in-medium nuclear effective interaction plays important role in various aspects like heavy-ion collisions,nucleosynthesis,as well as compact stars.The in-medium nuclear effective interaction is connected with the equation of state ?EOS?of nuclear matter.The isospin dependent part of EOS is known as ?high-order?symmetry energy.In this article,we investigate,in the framework of Skyrme effective interaction and Hartree-Fock self-consistent mean-field theory,the isospin effects on both ground state and dynamical properties of finite nuclei.For ground state properties of finite nuclei,our study mainly relates to the ground state binding energy.In particular,since the binding energy or nucleon separation energy depends on the symmetry energy,we find the neutron drip line and r-process path have a strong correlation with the symmetry energy at sub-saturation density E_sym(?_sc),where?_sc=0.11/0.16?₀.We then predict quite accurately the neutron drip line and r-process path by considering a recently obtained constrain of E_sym(?_sc).We also derive a semi-empirical mass formula with isospin quartic term,based on the studies on the double mass differences of finite nuclei,we extract a considerable fourth-order symmetry energy at saturation density,i.e.E_sym,4??₀?=20±4.6 MeV.Since most of the mean-field models give a quite small E_sym,4??₀?,such a large value of E_sym,4??₀?implies the importance of beyond mean-field effects in the determination of fourth-order symmetry energy of nuclear matter.For dynamical properties of finite nuclei,in order to investigate them in the framework of Skyrme interaction,we develop the lattice Hamiltonian Vlasov transport method.The lattice Hamiltonian Vlasov method has the advantage of ground state stability,as well as energy conservation.We also derive for Skyrme pseudopotential the single particle potential for transport calculation,and provide three Skyrme pseudopotentials which describe correctly both the EOS and single particle potential of nuclear matter.We calculated the isoscalar giant monopole resonance and isovector giant dipole resonance of⁹⁰Zr in the framework of Skyrme lattice Hamiltonian Vlasov method,the result are comparable with that of the random phase approximation.The isospin effects on the peak energy?centroid energy?and the electric dipole polarizability of isovector giant dipole resonance of⁹⁰Zr were also investigated,they are consistent with existing studies.Our result indicates the feasibility of adopting the lattice Hamiltonian Vlasov method in calculating dynamical properties of finite nuclei.The Skyrme lattice Hamiltonian Vlasov method developed in this article can be em-ployed into the medium-low energy heavy-ion reactions,and can be extended to higher energy region?1 GeV/A?.This will provide us more results on various areas like isospin physics and isotope production.