Systematic Study Of Nuclear Charge Radius

The nuclear charge radius is one of the most obvious and important nuclear parameters that give information about the deformation,the shell structure and the influence of effective interactions on nuclear structure.There are 908 experimental nuclear charge radii in the latest nuclear charge radius database.The number of proton in the range from 1 to 96,with a total of 92 elements.It is indicated that the measurement of the nuclear charge radius has been extended to the areas far away from the ?-stability line.This article investigates the empirical formulas of the nuclear charge radius and proposes new formulas,and then adopts machine learning to predict the nuclear charge radius.In this paper,combining with 885 experimental nuclear charge radii,we refitted the empirical formulas of nuclear charge radius and analyzed the microscopic effects of the nuclear charge radius.We found that the nuclear charge radius can be well described by introducing nuclear quadrupole moment into the empirical formula.The electric quadrupole moment is one of the deformation parameters,which reflects the degree of deviation of the sphere.Based on the experimental measurement values of the nuclear electric quadrupole moment,we add the electric quadrupole moment term into the empirical formula to reflect the nuclear deformation.Taking into account the relationship between the intrinsic electric quadrupole moment,the total spin and the electric quadrupole moment,we replace the electric quadrupole moment with the intrinsic electric quadrupole moment.Comparing the new formulas with the primary empirical formula,we found that the new formulas fits well with the nuclear charge radius.With the rapid development of hardware and data,some traditional methods have been replaced by machine learning.Machine learning methods is widely used in the field of physics.Adopting machine learning or neural networks to describe and predict microscopic physical quantities has become a novel method.Another work for this article is based on the Garvey-Kelson(GK)radius relationship and extends to the radius relationship between 25 nuclei.First,the charge radius of 894 nuclei is calculated by convolution,and then combined with the gradient descent method to training the 25 parameters by the convolutional neural network method.Finally,we selected four isotope chains of Ne,Ca,Zr and Pb in the forecast data,and calculated the root-meansquare deviation.We found that the results can reproduce the isotope shell effect and the odd-even staggering effect well.