The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.
Input-driven analysis in predicting nuclear charge radii using Monte Carlo dropout Bayesian neural network
School of Physics, Ningxia University（宁夏大学物理学院）；Key Laboratory of Beam Technology of Ministry of Education, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院教育部光束技术重点实验室）；Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University（广西师范大学核物理与技术广西重点实验室）
Bayesian Inference of High-density Nuclear Symmetry Energy from Radii of Canonical Neutron Stars
质量为1.4 M $_{\odot}$的中子星的半径$R_{1.4}$在最近的许多研究文献中一直被提取。利用具有代表性的$R_{1.4}$数据，我们推导出高密度核对称能$E_{\rm{sym}}(ρ)$和相关的核子比能$E_0(ρ)$在对称核物质（SNM）内的贝叶斯统计方法使用显式的同位旋依赖的参数状态方程（EOS）的核子物质。我们发现：（1）现有的天体物理数据已经可以大大提高我们目前对$ρ_0-2.5ρ_0$密度范围内物态方程的认识。特别地，在68%的置信水平下，在核物质饱和密度$ρ_0$的两倍处的对称能被确定为$E_{\mathrm{sym}}(2ρ_0)$ =39.2 $_{-8.2}^{+12.1}$ MeV。(2)精确测量的$R_{1.4}$单独与4\% 1 $σ$的统计误差，但没有系统误差将不会改善太多的约束条件的状态方程的致密丰中子核子物质相比，我们从使用现有的半径数据提取。(3)$R_{1.4}$半径数据和其他一般条件，如观测到的NS最大质量和因果关系条件，为高阶EOS参数引入了强相关性。因此，推断出的$E_{\rm{sym}}(ρ)$的高密度行为强烈地依赖于如何参数化高密度SNM EOS $E_0(ρ)$，反之亦然。(4)观察到的最大NS质量的值以及它是否被用作最小最大质量的锐截止值或通过高斯分布显著影响$E_0(ρ)$和$E_{\rm{sym}}(ρ)$两者的下…
Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions
从μ子原子的光谱实验中提取核电荷半径目前受到与核极化率效应的理论评估相关的大的不确定性的限制。为了便于计算，这些极化率校正通常表示为无量纲参数$η$的展开，在以前的文献中，已经论证了在轻核系统中保持0.33的近似值。在这项工作中，我们检查这一说法做贝叶斯分析的核极化率校正的兰姆位移在$μ^2$ H和$μ^3$ H原子和$μ^3$ He $^+$和$μ^4$ He $^+$在$η$ -展开的各种订单。我们的分析支持的说法，$η\ll 1$在这些系统中，并发现截断的不确定性是类似于以前的估计，唯一的例外是截断的不确定性在$μ^3$他$^+$离子，这被发现是更大的。
Predicting the moment of inertia of pulsar J0737-3039A from Bayesian modeling of the nuclear equation of state
我们从核物质状态方程的贝叶斯后验概率分布中研究中子星的转动惯量，该方程结合了微观多体理论和有限核的经验数据。我们把重点放在PSR J 0737 - 3039 A和预测，对于这个1.338 M_太阳中子星的转动惯量的范围$1.04 \times 10^{45}$ g cm $^{2} < I < 1.51 \times 10^{45}$ g cm $^{2}$在95%的可信度水平，而最可能的值为转动惯量的$\tilde I = 1.36 \times 10^{45}$ g cm $^{2}$。假设PSR J 0737 - 3039 A的转动惯量的测量精度为10%，我们研究了中子星半径和潮汐形变的影响。我们还确定了地壳的组成部分的转动惯量，并发现，对于典型的中子星质量为1.3 M_sun < M < 1.5 M_sun的地壳贡献的总转动惯量的1% - 6%，下面是需要解释的情况下，强中子夹带的脉冲星故障。
NucleiML: A machine learning framework of ground-state properties of finite nuclei for accelerated Bayesian exploration
Birla Institute of Technology and Science（比拉理工科学与技术学院）；Université Libre de Bruxelles（布鲁塞尔自由大学）；Universidad Andrés Bello（安德烈斯贝略大学）；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
