In this paper we study patterns of nuclear charge radii from three perspectives. The first is based on the so-called $\ensuremath{\delta}{R}_{i\mathrm{n}\ensuremath{-}j\mathrm{p}}$ relations, the root-mean-square deviation of which was reported to be 0.0072 fm for nuclei with both neutron number $N$ and proton number $Z$ $\ensuremath{\ge}8$, and are pointed out here to have actually a much smaller value, which is $\ensuremath{\approx}0.003$ fm for most nuclei with $N\ensuremath{\ge}28$ and $Z\ensuremath{\ge}28$. The second and third perspectives are new relations proposed in this paper. One is called the $\ensuremath{\delta}{R}_{\mathrm{nn}}$ relation enlightened from the so-called ``nonpairing'' interaction $\ensuremath{\delta}{V}_{\mathrm{nn}}$ in studies of nuclear binding energies, and the other is a linear dependence of nuclear charge radii in terms of valence nucleon numbers. All these relations are very accurate in most regions, and sizable deviations from these relations could be used to shed light on structural evolutions such as phase transitions and shape coexistence. About 830 unknown nuclear charge radii are enclosed in our Supplemental Material in this paper, with theoretical uncertainty below 0.03 fm.

中文翻译：

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核电荷半径的局部关系

在本文中，我们从三个角度研究核电荷半径的模式。第一个是基于所谓的 $\ensuremath{\delta}{R}_{i\mathrm{n}\ensuremath{-}j\mathrm{p}}$ 关系，均方根偏差为据报道，对于具有中子数 $N$ 和质子数 $Z$ $\ensuremath{\ge}8$ 的原子核来说，它是 0.0072 fm，这里指出它实际上具有更小的值，即 $\ensuremath {\approx}0.003$ fm 对于大多数具有 $N\ensuremath{\ge}28$ 和 $Z\ensuremath{\ge}28$ 的原子核。第二个和第三个观点是本文提出的新关系。一种被称为 $\ensuremath{\delta}{R}_{\mathrm{nn}}$ 关系，从所谓的“非配对”交互 $\ensuremath{\delta}{V}_{\mathrm {nn}}$ 研究核结合能，另一个是核电荷半径在价核子数方面的线性相关性。所有这些关系在大多数地区都非常准确，与这些关系的相当大的偏差可用于阐明结构演化，例如相变和形状共存。我们在本文的补充材料中包含了大约 830 个未知的核电荷半径，理论不确定度低于 0.03 fm。