Global charge radius predictions based on the mean charge density parameter

In this work, we introduced the Mean Charge Density Parameter (MCDP, denoted as [Formula: see text]) based on the Liquid-Drop Model (LDM) and the two-parameter Fermi model. Then we obtained 884 parameters for nuclei with [Formula: see text] 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[Formula: see text]fm. Considering the influence of the Casten and neutron-to-proton ([Formula: see text]) ratio on MCDP, the single parameter empirical formula is corrected by introducing these two factors, reducing the RMSD to 0.0649[Formula: see text]fm. Then by applying the [Formula: see text] to correct the empirical formula, the RMSD is reduced from 0.0649[Formula: see text]fm to 0.0263[Formula: see text]fm (the accuracy is increased by about 59%). Moreover, by training a Back Propagation neural network on the three factors (Casten, [Formula: see text], and [Formula: see text]), we constructed an MCDP predictor that reduces the RMSD to 0.0189[Formula: see text]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[Formula: see text]fm and 0.0181[Formula: see text]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.