Study Of Nuclear Charge Radii And Fission Barriers With WS~*Nuclear Mass Model

In this work, the nuclear charge radii and the fission barriers of heavy nuclei have been studied by using the Weisacker-Skyrme mass model. On one hand, a four-parameter nuclear charge radii formula was proposed by considering the shell and isospin effects. A new form I(1—I) for describing the isospin effect is introduced in the formula. We note that the rms deviation with respect to the885measured nuclear charge radii can be further reduced by about15%comparing with the result from the form IA1/3. To consider the shell effect, we introduce a correction termΔE A in the proposed formula, where ΔE is the shell correction of nuclei from the WS*mass model. With the microscopic shell correction, the rms deviation in the charge radii can be reduced by17%. Based on the proposed four-parameter nuclear charge radius formula, the known experimental datas are systematically investigated. The calculated rms deviation with respect to the885measured charge radii is only0.022fm with the proposed formula, which is smaller than the result of the HFB21model by15%. For the measured rms charge radii of343even-even nuclei, the rms deviation is0.016fm, which is significantly smaller than the result (0.026fm) of the RMF calculations. The results of magic nuclei, especially the parabolic charge radii trend in the Ca chain due to the shell effect is reasonably described with the formula. Furthermore, we predict the rms charge radii with the proposed formula for some super-heavy nuclei.The proposed nuclear charge radii formula is simultaneously applied for the study of shell evolution and nuclear symmetry energy. We find new magic number N=14,16based on the charge radii variation trend of Ne chain. On the other hand, the liner relationship between the slope parameter L of the nuclear symmetry energy and rms charge radius difference of the30S-30Si mirror pair is clearly observed. The estimated slope parameter is about L=54±19MeV from the coefficient of the isospin term in the proposed charge radius formula. In addition, we propose a method for calculating nuclear fission barriers based on the WS*nuclear mass model and existing experimental datas of fission barrier. We attempt to study the quadrupole deformation of nuclei at the quasi-saddle-point in the fission path. We find that the difference between quasi-saddle-point and ground state deformation decreases with the mass numbers A which can be reasonably well described by an analytical formula. Based on the formula for the deformation at the quasi-saddle-point, we calculate the fission barriers of prolate and spherical nuclei based on the potential energy surfaces from the WS*nuclear mass model. The rms deviation with respects to the112measured fission barriers falls to1.02MeV, which is smaller than the results of ETFSI model by40.7%. For the actinide nuclei, the rms deviation is only0.46MeV, which is smaller than the results of ETFSI model by37.8%. And we systematically calculated fission barrier heights for the prolate and spherical nuclei in the range of proton numbers98≤Z≤128and neutron numbers N≤200. The predicted central position of the super-heavy island could lie around N=176～178and Z=118～120according to the calculated fission barriers of nuclei, which is very close to the predicted position based on ground state shell corrections from the WS*nuclear mass model.