Evaluating nuclear charge radii based on the mean mass-density parameter using BP neural networks

In this paper, we have successfully obtained the mean mass-density parameter (rho m) using the nuclear masses AME2020 database and nuclear charge radius (CR) CR2013 database. The empirical formula is derived based on the relationship between rho m and N/Z (the ratio of the number of neutrons to protons). Subsequently, we obtained an empirical formula for the difference in rho m between two neighboring isotopes. By utilizing this empirical formula along with the AME2020 and CR2013 databases, we then calculated 625 charge radii for nuclei with N >= 21. The root-mean-square deviation (RMSD) between the calculated values and the experimental values in the CR2013 database is 0.0075fm. The predicted nuclear CR values are comparable to those of other researches, which some predictions closely matching the experimental values measured in recent years. Additionally, this work used the Back Propagation (BP) neural network to establish a model for describing and predicting the difference in the mean mass-density parameter between two neighboring isotopes. The RMSD between the calculated and experimental values obtained using this model is 0.0039fm. Some of our predicted values have good accuracy and compared well with experimental values. Both of the above methods indicate that the nuclear CR relationship proposed in this paper based on the difference in mean mass-density parameter has simplicity and reliability.