Study On The Uncertainty Of Nuclear Phenomenological Theory Model

The main work of this paper is to study uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field and the parameter fitting and uncertainty propagation of Bethe-Weizs（?）cker（BW）semi-empirical mass formula.The content is divided into two parts:Firstly,taking the heaviest doubly magic nucleus ²⁰⁸Pb as an example,the change of single particle energy level with parameters and degree of freedom of each deformation is studied systematically,and the uncertainty of single particle energy level and the statistical correlation between energy levels are investigated.Secondly,Bethe-Weizs（?）cker semi-empirical mass formula parameters and evaluation of binding energy uncertainty:based on the Bethe-Weizs（?）cker semi-empirical mass formula,we use the least square method to fit the experimental data AME2016 the nuclear mass table,obtain a new parameter group,and investigate the influence of parameter uncertainty on binding energy.Uncertainty analysis of single-particle energies in phenomenological mean field:This work take ²⁰⁸Pb as an example to study the uncertainty and statistical correlation of single particle energy levels based on the wood-saxon potential under the phenomenological mean field.First of all,we investigate the single particle energy level of the nucleus in the experiment,and the results calculated by the universal parameter group under the WS potential are obviously different from the single particle energy level in the experiment.The influence of the WS potential parameter on the single particle level is then explored and the percentage difference of the central potential depth V₀is given.Therefore,the variation of single particle energy level with parameters is discussed,the calculated parameter value when the single-particle levels is equal to the corresponding experimental single-particle levels is called the"best value".Taking the center potential parameter V₀as an example,the distribution of the parameter V₀"best value"can be obtained.Secondly,under the assumption that the WS potential parameters are independent of each other,we take the universal parameter group as the average value,given the standard deviation of each parameter,and use the Box-Muller method to produce the random number of parameters with gaussian distribution.Further,we calculate the single-particle energy levels under three types and give the distribution and uncertainty of energy levels when different parameters are uncertain.It seems that the energy uncertainty of the single-particle levels regularly evoluate with certain quantum numbers to a large extent for the given parameter uncertainties.In addition,the adjustment sensitivity coefficients of the energy levels of the three types of single-particle levels and the standard deviation of the single-particle levelsconsidering all parameter uncertainties are introduced,and the evolution properties are briefly discussed.Finally,in order to explore more comprehensively the statistical correlation characteristics between single-particle energy levels,the pearson correlation coefficients between any two energy of ²⁰⁸Pb levels proton and neutron are given in the range of parameter uncertainty.It was found that a positive,negative,or unrelated relationship may appear between two selected single-particle levels.Uncertainty analysis of Bethe-Weizsacker semi-empirical mass Formula:The Mass models is widely used in nuclear physics,and the error of the model may lead to the uncertainty of prediction,which should be taken into account when comparing with the experimental data.Firstly,we construct theχ2 function based on the nuclear mass table AME2016,using the least square method,and obtain a new BW semi-empirical mass formula parameter group by solving the linear equations composed of five variables.Secondly,the maximum likelihood method is used to obtain the distribution of the"best value"of parameters,and their standard deviation and correlation coefficient are given,and the influence of parameter uncertainty on the binding energy is discussed.Finally,according to the experimental energy and error,the uncertainty and correlation of parameters and the effect of the correlation of the parameters on the uncertainty of the binding energy are investigated by Monte Carlo method.