Predictions of charge density distributions for nuclei with $Z \geq 8$

Yun Dong Wang; Tian Shuai Shang; Hui Hui Xie; Peng Xiang Du; Jian Li; Haozhao Liang

nucl-thApr 7, 2026

Predictions of charge density distributions for nuclei with $Z \geq 8$

Authors: Yun Dong Wang, Tian Shuai Shang, Hui Hui Xie, Peng Xiang Du, Jian Li, Haozhao Liang

Organizations: College of Physics, Jilin University, Changchun 130012, China · Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan · Quark Nuclear Science Institute, The University of Tokyo, Tokyo 113-0033, Japan · RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Wako 351-0198, Japan

Abstract

A deep neural network (DNN) has been developed to accurately predict nuclear charge density distributions for nuclei with proton numbers $Z \geq 8$ . By incorporating essential nuclear structure features, the model achieves a significant improvement in predictive accuracy over conventional methods. The charge density distributions are analyzed using a Fourier-Bessel (FB) series expansion, and the DNN is trained on a comprehensive dataset derived from relativistic continuum Hartree-Bogoliubov (RCHB) theory calculations. The model demonstrates exceptional performance, with root-mean-square deviations of 0.0123 fm and 0.0198 fm for charge radii on the training and validation sets, respectively, remarkably surpassing the precision of the original RCHB calculations. Beyond advancing nuclear physics research, this high-precision model provides critical data for applications in atomic physics, nuclear astrophysics, and related fields.

Neural Surrogate Modeling

Neural surrogate modeling uses learned models to approximate costly simulations, enabling faster prediction, design, control, and inference.

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Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland · Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland · Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA+2

Multi-Task Learning

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Low-energy nuclear structure is encoded in a broad body of experimental information across the chart of nuclides. Learning how this information is organized across observables and nuclei can provide a data-driven empirical baseline for theoretical extrapolations and experimental design. Here, we develop held-out ensembles based on NuCLR (Nuclear Co-Learned Representations), a multi-task model of nuclear data, to study charge radii and electric-quadrupole transition strengths. Out-of-fold (OOF) validation shows that shared representation improves performance over single-task learning, yielding a charge-radius

\mathrm{RMS}

deviation of

0.0147~{\rm fm}

and a

\mathrm{B(E2)}

\mathrm{RMS}

deviation of

0.192~e^2{\rm b}^2

across hundreds of nuclides, competitive with state-of-the-art nuclear models. Our error bars estimate the expected prediction accuracy across the nuclear chart, highlighting regions where new data would encode information beyond the learned patterns. NuCLR thus serves as a data-driven surveyor of nuclear structure and a step toward a shared, multi-observable foundation model of the nuclear chart.

Abstract

Neural Surrogate Modeling

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