Shell Gaps And Symmetry Energy Coefficients In Nuclei

As one of the basic quantities in nuclear physics, the nuclear masses have attracted a lot of attentions for several decades. Up to now, the masses of only about 2400 nuclei have been measured in experiment. The masses of about 5000 nuclei are still unknown and need the predictions (extrapolation) from the global mass models. To accurately predict the masses of unknown nuclei, as many as possible mass-related observables should be investigated. Shell correction and symmetry energy play key roles in the description of the nuclear binding energy. As a measure of the discontinuity in the two-neutron separation energy at neutron magic numbers, the shell gap is a sensitive quantity to test the theoretical models and related to shell correction closely. In addition, symmetry energy coefficients of nuclei significantly influence the masses of nuclei near the neutron drip line. It is therefore necessary to investigate the shell gaps and symmetry energy coefficients of nuclei.In this thesis, we first systematically investigate the shell gaps in nuclei with eight different global mass models,.including the FRDM, HFB17, HFB27, DZ28, WS, WS*. WS3, and WS4 models. For unmeasured neutron-rich and superheavy regions, the un-certainty of the predictions from these different mass models is still large. The latest version (WS4) of the Weizsacker-Skyrme mass formula, in which the isospin depen-dence of model parameters is introduced into the macroscopic-microscopic approach inspired by the Skyrme energy-density functional, is found to be the most accurate one in the descriptions of nuclear masses, separation energies and shell gaps. We find that, for superheavy nuclei with N ≈ 200, the fluctuations in S2n are relatively large from the finite range droplet model (FRDM). The subshell closures at Z= 92,120 and N = 178 can also be observed in addition to the shell closures at the three evident magic numbers Z= 82,114 and N= 184. For light nuclei, the neutron shell gaps and deformation of Si, S, Ca, Ni isotopes from the WS model suggest that there exist neutron gaps at N= 14.16.32.40. These new "magic numbers" show strong proton neutron correlation. For example, at.N= 32. the shell gaps of 52Ca (Z= 20) is much larger than that of 60Ni (Z= 28).In addition, based on the semi-classical Thomas-Fermi approximation together with the Skyrme energy-density functional, we study the deformation dependence of symmetry energy coefficients of finite nuclei. The tests for the root-mean-square (rms) charge radii and deformation energies of Uranium isotopes indicate that the semi-classical ETF2 approach together with the Skyrme energy-density functional is appro-priate for the description of nuclear deformation energies. For spherical nuclei, from nuclei with mass number A= 20 to the nuclei with huge numbers of nucleons. of the order of 106, we study the mass dependence of the symmetry energy coefficients. With the extrapolations from the calculated results for finite nuclei, the asymptotic values of the symmetry energy coefficient J, of the binding energy per particle eu(∞) and of the coefficient asym(4)(∞) in the I4 term when A â†' ∞ arc close to the corresponding values from the asymmetric nuclear matter. For deformed nuclei, the symmetry energy coef-ficients asym of nuclei with A = 40,100.150,208 can also be extracted. We found that symmetry energy coefficients decrease with the increase of｜β2｜. The large ground state deformations for some nuclei can cause the change of the symmetry energy coefficients by about 0.5 MeV and the influence of nuclear deformations on the symmetry energy coefficients is more evident for light and intermediate nuclei. In the traditional liquid drop model. it is usually believed that only the surface energy and Coulomb energy terms are dependent on nuclear deformations. From the microscopic Skyrme energy density functional plus the ETF2 calculations. it is found that the isospin dependence of the difference between the proton and neutron diffuseness plays a key role for the deformation dependence of the symmetry energy coefficient of finite nuclei. These in-vestigations are not only important for the study of symmetry energy, but also for the improvement of nuclear mass models.