A nuclear periodic table

Abstract

There have been many empirical evidences which show that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an interaction among the nucleons. This leads to the concept of nuclear shells, similar to the electronic shells in atoms. In particular, the magic numbers due to closures of the nucleonic shells, corresponding to noble gases in elements, have been known to play an important role in nuclear physics. Here we propose a periodic table for atomic nuclei, in which the elements are arranged according to the known nucleonic shells. The nuclear periodic table clearly indicates that nuclei in the vicinity of the magic numbers can be understood in terms of a shell closure with one or two additional nucleons or nucleon holes, while nuclei far from the magic numbers are characterized by nuclear deformation.

On deformability of atoms—comparative study between atoms and atomic nuclei

“…ρ def,a (x, y, z) = ρ sph,a e β a x, e β a y, e −2β a z = ρ sph,a (r) + f (1) a (r) dρ sph,a (r) dr + f (2) a (r)…”

“…3r i r j − δ i j r 2 ρ (r) dr (i, j = x, y, z), (2) where ρ (r) is the density distribution. Note that there exist several normalizations for the quadrupole moment tensor Q.…”

“…On the other hand, in atomic nuclei, the inter-particle interaction is the attractive nuclear interaction between two or more nucleons, with no external potential. Despite the differences in the fundamental interactions, many similar properties have been observed in both systems, such as the shell structure and the associated magic numbers [2,3]. * Author to whom any correspondence should be addressed.…”

Three related topics on the periodic tables of elements

“…A nuclear periodic table, the "Nucletouch", in which elements are arranged based on the proton magic numbers of the nuclear shell structure, has recently been proposed (Hagino and Maeno 2020). As the last topic, we will introduce an additional remark not described in the original paper (Maeno and Hagino 2020): we will extend the comparison between the nuclear and atomic periodic tables shown in Figs.…”

“…Fig.9(a) Nuclear periodic table "Nucletouch"(Hagino and Maeno 2020), (b) atomic periodic table with the proton magic nuclei highlighted with bold character, and (c) a schematic to compare the atomic and nuclear shell structures.…”