Local relations of nuclear charge radii

Abstract

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.