We show that the charge radii of neighboring atomic nuclei, independent of atomic number and charge, follow remarkably very simple relations, despite the fact that atomic nuclei are complex finite many-body systems governed by the laws of quantum mechanics. These relations can be understood within the picture of independent-particle motion and by assuming that neighboring nuclei have similar patterns in the charge density distribution. A root-mean-square (rms) deviation of 0.0078 fm is obtained between the predictions in these relations and the experimental values, i.e., a precision comparable modern experimental techniques. Such high accuracy relations are very useful to check the consistence of the nuclear charge radius surface and moreover to predict unknown nuclear charge radii, while large deviations from experimental data are seen to reveal the appearance of nuclear shape transition or coexsitence.PACS numbers: 21.10. Ft, 21.90.+f, 27.70.+q, 29.87.+g Like many systems governed by the laws of quantum mechanics, the nucleus is an object full of mysteries whose properties are much more difficult to characterize than those of macroscopic objects. Rather than build an exact replica of the nuclear system (almost an impossible job), nuclear physicists in reality have selected a different approach, using a relatively small number of measurable properties of quantum systems to specify the overall characteristic of the entire nucleus. Investigations of these properties and moreover using them as bridges to reveal the atomic nucleus, form the basis of present nuclear physics investigations. Nuclear extension in space, often characterized by charge radius, is one of such static properties.Nowadays, nuclear size data [1] constitute one of the most precise and extensive arrays of experimental information available for the interpretation of nuclear phenomena. The pioneering works by using various methods such as electron scattering and muonic atomic spectroscopy [2], indicated that a nuclide near the β-stability line behaves like a solid sphere with constant density. In recent decades, the enormous progress in size determination of exotic nuclides has been entwined with the realization of radioactive ion beams [3] and fast developments especially in ultra-high-sensitivity laser spectroscopy techniques [4,5]. The new measurements contributed to revealing, for example, the neutron skin effect [6,7] and the nuclear shape variances [8][9][10] when moving far away from the stability line. These new results are among the strongest motivations for the next generations of nuclear physics facilities, in which electron-scattering experiments [11,12] on unstable nu- * Corresponding author: bhsun@buaa.edu.cn † ymzhao@sjtu.edu.cn clei are under way. In the march towards the new era of nuclear physics, the knowledge of nuclear sizes plays a very important role in understanding complex atomic nuclei.New precision data in turn challenge the present theories and trigger innovations to interpret the results and to understand underlying...
Abstract. The masses and sizes of nuclear ground states constitute two of the most precise and extensive arrays of experimental information. These data make a model-independent view of microscopic nuclear structure possible. Relevant differential observables of nuclear mass and charge radius can be highly sensitive to nuclear shape transitions. In this contribution, we examine the correlation of these two bulk properties to nuclear shape transitions. By combining different observables, it is even possible to isolate shape transitions from nuclear shell closures.
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