An Improved Nuclear Mass Formula

In this thesis we propose an improved nuclear mass formula based on the macroscopic-microscopic method and the Skyrme energy density functional. Simultaneously, we study some ground properties of nuclei with the proposed model. The main improvements include: (1) We introduce a mass- and isospin-dependent correction term to the symmetry energy coefficient. This term approximately describes the surface-symmetry energy and the Wigner effect. Compared with the case that this term is not taken into account, the rms deviation of nuclear masses for the 2149 nuclei is reduced. Furthermore, we find when the isospin-dependent of the symmetry energy coefficient is taken into account, the obtained optimal symmetry energy coefficient Csym of nuclear matter increases from 26.7MeV to 30.0MeV, which is more reasonable. (2) We investigated the energy of a nucleus with respect to deformations based on the Skyrme energy density functional, together with the extended Thomas-Fermi approximation (ETF), the mass-dependent curvatures of the parabolas bk. which greatly reduces the computation time for the energy calculation of deformed nuclei. (3) We introduce a scale factor c1 to the shell correction. This additional parameter is used to adjust the division of the binding energy between the macroscopic part and the remaining microscopic correction. We find that the rms deviation can be further reduced. (4) For nuclear matter we investigate the relation of symmetry potential Vsym and the symmetry energy coefficient csym, find that they are close to each other approximately. Then for finite nucleus we investigate the relation of the isospin-asymmetric part Vs of the single-particle potential and the symmetry energy coefficient asym and also find that they are equal approximately. So we empirically set and assume Vs≈asym in the improved mass formula not only for simplification but also for increasing the consistency of the model parameters between the macroscopic and microscopic parts. We obtain the improved mass formula set labeled as WS. Based on the WS, we further improve the nuclear mass formula. (5) The Coulomb energy form is slightly changed, Z(Z-1) is replaced by Z2, following the form in the finite-range droplet model (FRDM). This modification can slightly improve the rms deviation of nuclear mass by about 2～3%. (6) According to the constraint between the shell corrections of the mirror nuclei, we introduce a correct term |Ⅰ|E'hto the nuclear shell correction energy, and find that this term can considerably reduce the rms deviation of nuclear masses by about 10%. (7) Theβ6 deformation of nuclei is taken into account, which slightly improves the results of heavy nuclei. The nuclear mass formula including the improvements mentioned is labeled as WS*.Compared to the finite range droplet model, the rms deviation with respect to 2149 mea-sured nuclear masses is reduced by 33%, falling to 0.441MeV. The rms deviation of the neu-tron separation energies of 1988 nuclei falls to 0.332MeV, the corresponding result of FRDM is 0.399MeV. Additionally, the number of parameters in the model is reduced from 31 to 15 (including the two parametersγand p used in the strutinsky procedure). Compared to the standard Hartree-Fock Bogoliubov(HFB) approach, the obtained rms error of WS* for the measured 2149 masses and the 1985 neutron separation energies are obviously smaller than those of HFB calculations and the CPU time for calculations of the whole nuclear chart is much shorter.Finally, some ground properties of nuclei, such as the shell corrections, the deformations, the neutron/proton drip lines, the shell gaps of nuclei, fission barriers, and theα-decay energies of some super-heavy nuclei have been studied with the proposed model. Simultaneously the calculated results from other models (FRDM, HFB17) and the experimental data are also presented for comparison. The predicted central position of the superheavy stability island according to the calculated shell corrections of nuclei with WS* model could lie around N= 176～178 and Z=116～120. The shell corrections of superheavy nuclei (in absolute value) are close to the corresponding fission barriers of the nuclei from other macroscopic-microscopic model. Additionally, the shell gaps at proton magic numbers Z=20,28,40,50,82 can be remarkably well described with the proposed model. The rms deviation of theα-decay energies of 46 superheavy nuclei is reduced from 0.566 MeV with FRDM to 0.263 MeV with the proposed model in this work.