Application Of Skyrme Energy Density Functional To The Properties And Reaction Of Nuclei

The energy density functional theory is widely used in many-body problemfor it offers us with a reasonable balance between the accuracy and computationalcost. We have applied the Skyrme energy density functional to calculate theneutron skin thickness of nuclei and explore the relation between the neutronskin thickness and the equation of state (EOS). We further apply the Skyrmeenergy density functional to study the heavy-ion fusion reaction.Based on the Skyrme energy density functional and the Thomas-Fermi ex-pressions of the kinetic energy density, we calculate the ground state energiesand the density distribution by using the restricted density variational method.According to the Hohenberg-Khon theory, all the ground state properties ofa nucleus can be uniquely determined by the density distribution of groundstate. We have checked the ground state energies, the density distribution ofprotons and neutrons, the root-mean-square radii of charge distribution, pro-ton and neutron distribution for series nuclei by using the restricted densityvariational method. Our calculated results can reproduce the experiment datawell. This makes us able to calculate the the neutron skin thicknesses of nuclei(â–³r_np=＜r_n²ï¼ž^1/2-＜r_p²ï¼ž^1/2) and study the relation between the neutronskin thicknesses of neutron-rich nuclei and the isospin dependent part of the ef-fective interactions. The neutron skin thickness for ²⁰⁸Pb, ^112-124Sn, ⁴⁸Ca,⁹⁶Zr, ¹⁸O are calculated with 47 Skyrme interactions available up to now. Ex-ploring the relations between the neutron skin thickness and L=3_ρ0((?)e_sym)/(?)|_ρ=ρ0K_sym=9_ρ0²((?)²e_sym)/(?)ρ²|_ρ=ρ0 and a_s which are the slope, curvature of the symmetryenergy near the saturated density, and the symmetry energy coefficient respec-tively. We find that the neutron skin thickness increases with the stiffness ofthe symmetry energy which is closely related to the nucleon-nucleon interac-tion. Our study indicates that the model independent neutron skin thicknessdata are especially important for providing accurate information of the densitydependence of the symmetry energy of nuclear matter. By calculating the neu- tron skin thickness of nuclei with Z=8～120, A=5Z/3～3Z, wefind that the neutron skin thickness depend on the isospin asymmetry degreeδof the system linearly i.e.â–³r_np=-0.053+1.016δ, which is in agreementwith the relation ofâ–³r_np=(-0.04±0.03)+(1.01±0.25)δ, extracted fromthe measurements by antiproton annihilation method. By fitting data from themeasure of antiproton annihilation method, we get the ranges of the slope, cur-vature of the symmetry energy near the saturated density (L, K_sym) and thesymmetry energy coefficient a_s. A_s, L and K_sym are from a_s=30～35MeV,L=20～100MeV, K_sym=-256～70MeV. The Skyrme parameters SLy0-SLy10, SkM^*, SkP, SLy230a, SkMP, SKT1-3, Ski3, MSk1-2, SII are in theabove ranges. Most of them are proposed recently.Heavy-ion fusion reaction are another useful method to explore the nucleon-nucleon interaction. We apply the Skyrme energy density functional to studythe heavy-ion fusion reaction. With the obtained proton and neutron densitydistributions, the fusion barriers of a series of reaction systems are calculated bythe same Skyrme energy density functional. We propose a parametrization forthe weighing function of the fusion barrier and based on the calculated fusionbarrier we calculate the fusion cross sections by means of barrier penetrationmodel. Fusion excitation functions for more than 50 systems are calculated withour model. A large number of measured fusion excitation functions spanning thefusion barriers can be reproduced well. The competition between suppressionand enhancement effects on sub-barrier fusion caused by neutron-shell-closureand excess neutron effects is studied also. In order to get the information ofthe nuclear equation of state (EOS) in terms of the fusion reaction, we furtherexam 47 Skyrme effective interactions which correspond to different EOS. Wehave calculated the fusion barriers for ⁹⁰Zr+⁹⁰Zr, ⁹⁰Zr+⁹²Zr, ⁹⁰Zr+⁹⁶Zr,⁶⁴Ni+⁶⁴Ni reaction systems respectively. Comparing with the calculated fusionbarriers with" M3Y+repulsive core" effective interaction, we find that the Skyrmeinteractions of which the incompressibility coefficients k_∞are in the range of220±20MeV may give a reasonable fusion barrier. We propose an incident energydependent barrier parameter hω₀(E) to describe the curvature of the inverseparabola which is used to replace the calculated fusion barrier approximatively. Based on the Wong's formula and our parametrization, method, we calculate thefusion cross sections for ⁹⁰Zr+⁹⁰Zr,⁹⁰Zr+⁹²Zr,⁹⁰Zr+⁹⁶Zr, ⁹⁰Zr+⁹⁴Mo,⁹⁰Zr+⁸⁹Y reaction systems and find that the steep falloff of fusion cross sections atextreme sub-barrier energies can be reproduced well when the Skyrme interactionSLy4 is adopted.