The Nuclear Liquid-drop Model Parameters And Their Uncertainties

As one of the basic quantities in nuclear physics, the nuclear mass has always been the hot spot of the nuclear physics research for many years. 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 theoretical mass models. To accurately predict the masses of unknown nuclei, as many as possible mass-related observables should be investigated. The binding energy per nucleon is an important measurement quantity of the nuclei mass formula, which offers a vital bridge between the macroscopic-microscopic mass formula and the Skyrme energy-density functional, helping us obtain the equation of state(EOS) from the point of the nuclear mass. In addition,the important physical quantity in the study of nuclei symmetry energy named reference densityp^, can connect the symmetry energy of nuclear matter with that of finite nuclei closely. For example,the reference density of 208Pb is about 0.1fm-3, which means that Eaym(0.1fm-3)=asym(208Pb). The physical mechanism behind the reference density remains not very clear so far, it still needs us further research therefore.In this thesis,firstly, we extract liquid drop model parameters based on the Skyrme energy density functional together with the extended Thomas - Fermi approach(ETF2). We investigate the binding energy per nucleon with 79 different Skyrme forces system-atically, the mass number from A=20 to A = 106 are included in the nuclear system of the corresponding values. Then we extende the binding energy per nucleon in terms of A-1/3 in the nuclei liquid-drop formula. the coefficients of volume,suface,and cur-vature terms can be gained easly, the values of them are av=-15.90 ± 0.21MeV,as= 17.15±1.02MeV and acur=3.07±0.51MeV respectively. These values are similar with both LSD and WS* model’s. We compare the binding energy per nucleon of infinite nuclear matter e∞ with the values of av extracted from the extended Thomas - Fermi approach of finite nuclei, finding that the latter are quite similar with the values of e∞, the difference between the results from the two methods is only 26 keV. This indicates that extracting the liquid drop model parameters by the extended Thomas-Fermi approach(ETF2) is quite reliable. Furthermore,we also investigate the average density of finite nuclei, discovering that whether light or heavy nuclei, both the average density of the nuclear surface area and the reference density of symmetry energy are consistent with each other. It provides strong evidence for explaining the physical mechanism behind the reference density.Finally, based on the Weizsacker-Skyrme(WS*)nuclei macroscopic-microscopic mass model, we investigate the uncertainty of model parameters. We seek the optimal value for more then 2000 different nuclei by changing one of the parameters and keeping the others constant. In the same way we explore the 13 parameters of WS* model one by one. These optimal values of more then 2000 measured nuclei eventually form a statistical distribution for the parameter. We find that the uncertainties of the pairing correction coefficient apair, the depth of single particle potential V0 andspin - orbit potential parameter λ0 are larger then the others. These studies are helpful to further improving the WS* mass formula.