The Study Of The Ground State Of Nuclei Based On An Improved Mass Formula And Skyrme Model

Nucleus is regarded as a many-body system,this work is studying the ground-state properties of nucleus by using two theoretical models both developed from a type of liquid drop model(LDM)based on the saturation and incompressibility of nuclei:(1)an macroscopic-microscopic mass model derived from the traditional LDM,in which nucleons are regarded as molecules.(2)Skyrme model extracted from the ”Mesonic Fluid” model with the nucleons being some kind of local twists in the fluid.There are three main work in this thesis:The first main work of this thesis is studying nuclear binding energy by using an improved mass formula.Nuclear mass as one of the main ground-state properties of nucleus,can connect lots of hot topics in nuclear physics and other branch.While it is difficult to directly measure the binding energy of boundary nuclei.Then the common way to extrapolate the values is using mass formula.By considering a general and a modified radial basis function(RBF)correction respectively into the Weizs¨acker-Skyrme-Type(WST)nuclear mass model,the root-mean square(rms)deviations of the selected known 2267 nuclei,under two new improved WST model with a general/modified RBF correction,are dropped from 493 ke V to 323/167 ke V.Furthermore extracting one-nucleon and two-nucleon separated energy,?-decay and ?-decay energies,the odd-even staggering(OES)from the calculated binding energy,the rms of the mentioned physical observables are reduced about 200-300 ke V.Finally,We extrapolate the binding energies of 12435 nuclei(8 ? Z ? 128 and 8 ? N ? 251)by using the improved WST model with the modified RBF correction.Meanwhile,onenucleon and two-nucleon separated energy(Sn,p,2n,2p),? and ?-decay energies(Q? and Q?-,?+,EC),pairing gap ?n and ?p as well as the ground state deformations ?2,4,6and all the aspects of the WS-Type mass model are showing in this thesis.The second one in this thesis is about Skyrmion.Skyrme model developed from mesonic fluid model is an effective hadronic theory and be regarded as a low energy approximation to QCD.Skyrmion is the topological soliton solution of Skyrme model which both topologically and energetically stable.Quantized Skyrmion can be used to study nucleus.Here,we considering a BPS-Skyrme term and a loosely bound potential into the general Skyrme model.The rational map approximation are firstly introduced into the BPS-Skyrme term.Finally we study the variation of the relative classical and total binding energies,model parameters,nucleon mass in the parameter space,we find classical binding energies as low as 1.8%.The last work in this thesis is about considering the coulomb effect into the Skyrme crystal in which 4-Skyrmion is the subunit if one added the ?mass term.The mentioned two models both developed from the drop model,the energy of Skyrmion contained the volume term,surface term and asymmetry term compared with the mass formula,while this is no Coulomb effect in Skyrme model and leads to Skyrmion can not better to describe the heavy and superheavy nuclei.It is the first time to calculate the Coulomb energy by using an point approximation for 4-Skyrmion,8-Skyrmion,12-Skyrmion and other Skyrmion known the ground-state structure of nuclei.Finally using the known results to fit an expression of Coulomb energy in the Skyrme model and compare with the contribution of Coulomb effect in mass formula,both results showing a good consistency.