Isospin Symmetry And Local Equations Of Nuclear Masses

In this thesis we propose an improved version of the Weizacker-Skyrme mass formula WS3by considering some residual corrections. The residual corrections include:(1) an empirical correction term in liquid-drop energy which is to consider the Wigner-like effect of heavy nuclei. This term is due to the approximate symmetry between valence proton and valence neutron. It mainly describes the Wigner effect of heavy nuclei, and reduces the rms deviation with respect to masses by about5%.(2) Some other residual corrections caused by the microscopic shell effect, in which△M is to further consider the mirror nuclei effect,△P is for describing the residual pairing corrections and△T for the residual deformation effect of nuclei.The rms deviation with respect to2149measured nuclear masses is reduced to336keV and that of the1988measured neutron separation energy is reduced to286keV. So far, it is the one of the best global nuclear mass formulas. In addition, the rms deviation with respect to α-decay energies of46super-heavy nuclei from the WS3model reaches248keV, which is much smaller than the result (936keV) of the DZ28model. The difference between the calculated α-decay energies of the super-heavy nuclei and the measured data is within△Qa=±0.4MeV for odd-Z nuclei, and the corresponding results from Sobiczewski and FRDM are±0.8and±1.0MeV, respectively. Comparing with some widely used global mass formulas, the number of the model parameters in WS3is smaller, and the prediction power is stronger. Furthermore, the proposed formula can reproduce both the Garvey-Kelson (GK) relations and the isobaric multiplet mass equation (IMME) reasonably well.Simultaneously, we investigate some local mass equations such as the Garvey-Kelson relations and the isobaric multiplet mass equation. It is found that the rms deviation of GK relations decreases with the increasing of the times n of GK relations adopted when calculating the masses of nuclei around the β-stability line. The rms error can reach86keV. To check the application of the GK relations on neutron-rich nuclei, we calculate the masses of some extremely neutron-rich nuclei by GK relations and surprisingly find that the rms deviation increases rather than decreases with the increase of the time n of GK relations. The calculations imply that the prediction power could be reduced when the GK relations are applied with an iteration fashion for the calculation of the masses of extremely neutron-rich nuclei.Based on the systematic investigations, we find that the predict power of the local equations relates closely to the average distance <R> between the nuclide to be studied and the reference nuclides on the nuclear mass surface involved in the GK relations, and the times n using the GK relations. On one hand, the larger the value of average distance is, the larger the corresponding rms deviation is, when the value of n is fixed. On the other hand, the rms deviation of nuclear masses seems to decrease with the increase of n when the average distance is fixed. For a further test of the reliability of different mass models, the isobaric multiplet mass equation (IMME) is adopted. Based on six different mass models, we find that the rms deviation between models and experiment data decrease with the rms deviation between the models and IMME, which suggests that the IMME could be used as a useful tool for testing model reliability. In addition, with a systematic study of17global nuclear mass models, we find that fulfilling both the IMME and the GK relations seems to be two necessary conditions for improving the quality of the model prediction.