Shell quenching in nuclear charge radii based on Monte Carlo dropout Bayesian neural network

Charge radii can be generally used to encode information about various fine structures of finite nuclei. In this work, a constructed Bayesian neural network based on the Monte Carlo dropout approach is proposed to accurately describe the charge radii of nuclei with proton number $Z\geq20$ and mass number $A\geq40$. More motivated underlying mechanisms are incorporated into this combined model in addition to the basic building blocks with the specific number of protons and neutrons, which naturally contain the pairing effect, the isospin effect, the shell closure effect associated with the Casten factor $P$, the valence neutrons, the valence protons, the quadrupole deformation $β_{20}$, the high order hexadecapole deformation $β_{40}$, and the local shape staggering effect of $^{181,183,185}$Hg. To avoid the distorted cases of the traditional Casten factor at the fully filled shells, the modified Casten factor $P^{*}$ is introduced into the input structure parameter sets. The standard root-mean-square deviation is reduced to $0.0084$ fm for the training data set and $0.0124$ fm for the validation data set with the modified Casten factor $P^{*}$. Meanwhile, the shell closure effect of nuclear charge radii can be reproduced remarkably well. We have successfully demonstrated the ability of this constructed model to significantly increase the accuracy in predicting the nuclear charge radii.