Zhen-Yan Xian | Searcharxiv

arXiv2026

Input-driven analysis in predicting nuclear charge radii using Monte Carlo dropout Bayesian neural network

Nuclei charge radii play an essential role in understanding the fundamental interactions of finite quantum fermion systems. In this work, input-driven Bayesian neural network based on the Monte Carlo dropout approach has been built to characterize the systematic evolution of charge radii of nuclei with proton number $Z\geq20$ and mass number $A\geq40$. The motivated underlying mechanisms have been introduced into the input structures, which contain pairing effect, isospin asymmetry degree, the correlations between the valence nucleons and valence holes for neutron and proton, quadrupole deformation parameter $β_{20}$, and the local shape staggering phenomena of $^{181,183,185}$Hg isotopes.In addition, shell quenching effect is also taken into account by incorporating the modified Casten factor $P^{*}$ into the input structure. The quadrupole deformation parameters $β_{20}$ derived from finite-range droplet model (FRDM), relativistic mean field (RMF) theory and Weizsäcker-Skyrme (WS) approach are employed to analyze the local variations of nuclear charge radii.The hyperparameter is adjusted automatically in the constructed model.The calibrated results give comparable root-mean-square deviations (RMSD) in the training and validation sets with various shape deformation inputs. The abrupt increase in charge radii around N=60 is well reproduced along Z=37-40 isotopic chains, but this trend is less pronounced along Z=36 and 41 chains. This provides a indicator to confirm the rapid shape-phase transition regions around N=60 from the perspective of finite nuclei size. Shell quenching effect of charge radii along the bismuth isotopes are reproduced well at N=126, but slight deviations can be encountered due to the absence of high-order octupole deformation around N=130 regions and shape-staggering phenomena toward neutron-deficient regions, respectively. This means that...

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arXiv2025

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.

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