Study of nuclear charge radius
Authors: Cao Ying-Yu , Guo Jian-You ,   School of Physics and Materials Science, Anhui University, Hefei 230601, China
Published: December 2020

Based on the existing experimental data of nuclear radius, the previous formula of nuclear charge radius is verified and discussed. Comparing the formula of the single-parameter nuclear charge radius, it is proved that the formula of <inline-formula><tex-math id="M4">\begin{document}$Z^{1/3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M4.png"/></alternatives></inline-formula> law is better than the formula of <inline-formula><tex-math id="M5">\begin{document}$A^{1/3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M5.png"/></alternatives></inline-formula> law. We refitted the two-parameter formula and the three-parameter formula that have been proposed and confirmed that the two-parameter and three-parameter formula fit better than the single-parameter formula. It is shown that show that the deformation plays a key role in the nuclear charge radius. The electric quadrupole moment is an important physical quantity representing the properties of the nucleus. Its appearance indicates the deviation from spherical symmetry and also reflects the size of the nuclear deformation. The electric quadrupole moment is also one of the basic observations to understand the distribution of matter within the nucleus, to examine the nuclear model, and to observe nucleon-nuclear interactions. Taking into account the relationship between the nuclear quadrupole moment and the deformation, the electric quadrupole moment factor is added to the original three-parameter formula to obtain a new formula for the nuclear charge radius. Fitting the four-parameter formula, it is found that the theoretical value of the nuclear charge radius is in good agreement with the experimental value, the root-mean-square deviation is 0.0397 fm. Considering the relationship between the total spin and the electric quadrupole moment, the intrinsic electric quadrupole moment is obtained and brought into the formula for fitting, and the root-mean-square deviation further decreases,the root-mean-square deviation is 0.0372 fm. Finally, considering the universality of odd-even staggering, we add the <inline-formula><tex-math id="M6">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M6.png"/></alternatives></inline-formula> term that can reflect the odd and even oscillation phenomenon, and the root-mean-square deviation obtained by the formula is 0.369 fm, which better reflects the relationship between the deformation and the nuclear charge radius. Compared with the formulas already proposed, the new formula can better reflect the variation trend of nuclear deformation, shell effect, odd-even staggering, etc., and the calculation accuracy is also improved, which can provide a useful reference for future experiments.