Abstract
In this paper, we study the nuclear charge radius for 804 nuclei with Z,N≥12 in the CR2013 database (excluding the isotopic chains of Tb, Tm, Lu and Cm). By adding the Casten factor for the Z1/3 law empirical formula to calculate the charge radii of these nuclei, the root mean square deviation (RMSD) between calculated and experimental values is 0.0530fm. A new empirical formula is then obtained by correcting using neutron–proton ratio factor N/Z and the neutron factor 1/N. The RMSD between the calculated values obtained using this new empirical formula and experimental values is 0.0197fm. The new empirical formula reproduces well not only the factors’ (i.e. the N/Z and 1/N factors) dependence on charge radii, but also the kinks of charge radii at the neutron magic numbers N = 82 and 126 for some isotope chains. Furthermore, this paper introduces the Back propagation (BP) neural network approach using the Casten factor, the N/Z factor and the 1/N factor as input variables to train the model. The RMSD between the calculated values obtained by the neural network model II and the experimental values is only 0.0098fm. Compared to the empirical formula, the RMSD of the neural network model is reduced by 50%. The above research results based on the improvement of the Z1/3 law formula indicate that the relation and models proposed in this paper have accuracy and reliability.
