Investigation Of Nuclear Properties And Parameter Uncertainties Based On Macroscopic-Microscopic Model

Nuclear structure is an important research field in nuclear physics,which mainly studies a series of properties of nuclear ground state and low excited state.As one of the basic properties of the nucleus,the nuclear mass(binding energy)directly reflects the results of the strong interaction,weak interaction and electromagnetic interaction in the nucleus,and plays a crucial role in the study of nuclear structure,low energy nuclear reactions and astrophysics.Recently,the accuracy of its measurement and calculation has important consequences in different areas,like the determination of fundamental constants,symmetry violations,metrology,stellar evolution,and nucleosynthesis.Theoretically,the global Bethe-Weizsacker(BW)mass model can reproduce the nuclear mass well,and the study of the uncertainty of model parameters is of great significance to evaluate the predictive power of the model.Nuclear properties and parameter uncertainties have been investigated in macroscopic-microscopic frameworks in terms of pairing self-consistent Woods-Saxon-Strutinsky calculations(e.g.,the PotentialEnergy-Surface method and the total-Routhian-surface method)in this thesis.In this thesis we study several issues based on BW mass model as follow:Firstly,based on AME2016 experimental data,the least-square method has been used to re-fit the parameters of three BW mass models.By random number sampling method,model parameters and uncertainties are studied in a large sample space.It is found that the statistical correlation of mass model parameters has an important impact on the theoretical binding energy uncertainty.The influence of statistical correlation of model parameters on the theoretical binding energy uncertainty is quantitatively given.Taking 208Pb as an example,the influence of statistical correlation of parameters on the theoretical binding energy error is more than a hundred times different.Then,it is found that the uncertainty of the model parameters has strong dependence on the modes and values of the three common experimental binding energy errors,but the statistical correlation of the parameters is weak.Secondly,the two BW semi-empirical mass models were improved by combining PES systematic calculation and considering adding different effects.It was found that the total square root value of experimental and theoretical binding energy decreased from 2.5 MeV to about 0.6 MeV after the model improvement.The parameter correlation and error transfer of the improved model are also studied.The uncertainty of theoretical binding energy is also given for the improved model considering the statistical correlation of parameters and the error transfer relation.Thirdly,a new method for estimating model parameters and errors is proposed based on the method of exact solution.It is found that the distribution of model parameters is Cauchy distribution.Since the expected value of this distribution does not exist,we use the maximum likelihood method to get the corresponding model parameters and parameter errors of the position parameters and scale parameters of the Cauchy distribution.It is found that the theoretical binding energy of 208Pb is composed of two Cauchy distributions with different scale parameters,and the error range is reasonable and the confidence level is high.The theoretical error of the calculation results of the whole nucleus is within a few full width at half maximum(FWHM).This method improves the predictive ability of the mass model to a certain extent.Fourthly,the structural properties of even-even nuclei along the β-stability line are systematically analyzed and investigated by means of our improved six-parameter mass model.As is known,the quadrupole deformation parameter β2 can be obtained not only from reduced transition probabilities B(E2)but also from experimental quadrupole moment values Q.The quadrupole deformationβ2 values calculated by PES method are more similar to those obtained by quadrupole moment values which are not considering nuclear surface vibrations.However,the experimental results with vibration effect can better reflect the real deformations.Based on the systematic law of two-nucleon separation energies,the bound limit of even-even nuclei is crudely estimated along the stability line.The yrast states are the lowest energy state for a given spin and can reflect many interesting phenomena,such as band crossing,yrast traps,shape and phase transition.It is possible for the collective motion mode between vibration and rotation of a nucleus alone the yrast line theoretically,however,the evolution phenomenon from rotation to vibration has not been observed experimentally.An empirical approach,called E-GOS(E-gamma over spin)curves,which is used for discerning the evolution between vibration and rotation in nuclei as a function of spin,is discussed,and the insufficiency of the vibration-like criterion of the E-GOS curves to determine the transition from rotation to vibration is emphasized.We clarify this problem in terms of the shape,moment of inertia,angular momentum and potential energy surface variation with the rotational frequency of some typical nuclei.Our study shows that the reason for this "vibrationlike" phenomenon may be due to the strong interaction between the ground-state band and the S band,thus eliminating the misunderstanding about the evolution of rotation to vibration.Moreover,the high-spin phenomenon of some typical γ-deformation nuclei have been studied,and the deformation and rotational frequency dependence of single particle energy level are briefly analyzed.In addition,we also studied the components of Woods-Saxon wave function and the uncertainty of single particle energy level,and found that the uncertainty of potential parameters has a direct effect on the uncertainty of single particle energy level.