Global charge radius predictions based on the mean charge density parameter

In this work, we introduced the mean charge density parameter (MCDP, denoted as 𝜌) based on the liquid-drop model (LDM) and the two-parameter Fermi model. Then we obtained 884 parameters for nuclei with Z, N ≥ 8 from the CR2013 database. The study yielded a simple empirical formula for single parameter based on these parameters. The root-mean-square deviation (RMSD) between the calculated values by using this empirical formula and experimental values in CR2013 database is 0.0725 fm; Considering the influence of the Casten and neutron-to-proton (N/Z) ratio on MCDP, the single parameter empirical formula is corrected by introducing these two factors, reducing the RMSD to 0.0649 fm; Then by applying the 1/N to correct the empirical formula, and the RMSD is reduced from 0.0649 fm to 0.0263 fm (the accuracy is increased by about 59%). Moreover, by training a Back Propagation neural network on the three factors (Casten, N/Z, and 1/N), and we constructed an MCDP predictor that reducing the RMSD to 0.0189 fm (the precision has been improved by approximately 28%). Finally, when the predictions from the refined empirical formula and the BP-neural-network model are confronted with 129 recently measured charge radii, the RMSDs are 0.0215 fm and 0.0181 fm, respectively. In summary, the results confirm the feasibility, stability, and accuracy of the charge radius framework using the newly introduced mean charge density parameter.