In this paper, we construct a nuclear periodic table based on the shell structure of protons. In this regard, we would like to point out that the occurrences of the magic numbers are not explicitly presented in a standard nuclear chart, which shows only the abundance ratio or the decay half-life for each nuclide. Nevertheless, it might still be useful and pedagogical to construct a nuclear periodic table e.g., in order to visualize the difference in magic numbers between nuclear systems and electronic systems. Such a map would be more useful than a one-dimensional ( Z or N) periodic table in order to classify detailed properties of atomic nuclei. 2018), which can be used to learn e.g., the abundance fraction of each stable nuclide and a lifetime of each unstable nuclide. As a matter of fact, a two-dimensional map on the NвЂ“ Z plane, known as a nuclear chart, is widely known for atomic nuclei (Koura et al. Of course, atomic nuclei consist of two different kinds of particles, that is, proton and neutron, and thus their properties cannot be determined solely by the number of protons Z (or of neutrons N). The aim of this paper is to present such nuclear periodic table, based on the shell structure of atomic nuclei. Since magic nuclei, that is, nuclei with a shell closure of neutron or proton, correspond to noble gases in the elements, one may expect a similar periodic table for nuclei to the one for the elements. The magic numbers due to the shell closures are also indicated The ordering of the levels within each shell may be altered depending on the number of protons and neutrons.

Because of a strong spin-orbit interaction, a single particle level with an orbital angular momentum l splits into two levels with the total angular momentum of j = l в‘/2, among which the level with j = l + 1/2 is lowered in energy than the level with j = l - 1/2. The degeneracy of each single-particle level is given by 2 j+1. For example, 1 d here is equivalent to 3 d in the electronic notation. Note that the radial quantum number n is different from the principal quantum number n p= n+l, which is often used to label electronic single-particles levels. correspond to l = 0, 1, 2, 3, 4, 5вЂ¦, respectively. These are labeled by the quantum numbers n, l, and j, where n is the radial quantum number, that is, the number of nodes (plus 1) in the radial wave function, l is the orbital angular momentum, and j is the total angular momentum due to the addition of the orbital and spin angular momenta. Typical single-particle levels of nucleons in a spherical mean-field potential. These magic numbers have been explained using a finite depth potential with a strong spinвЂ“orbit interaction, as is shown in Fig. For stable nuclei, it has been known that the shell closures occur when the number of neutron or proton takes the so called magic numbers given by 2, 8, 20, 28, 50, 82, and 126. Such shell structure in atomic nuclei have been evidenced by many phenomena, such as an increased binding energy, discontinuities of the nuclear radius as well as neutron and proton separation energies (corresponding to the ionization energy in atoms), and an increased excitation energy of the first excited state, all of which occur at the shell closures. In this picture, nucleons occupy single-particle orbits, like electrons in atoms, which naturally leads to the concept of shell structure and shell closures. It has been known that many properties of atomic nuclei can be understood in a simple mean-field approximation, in which nucleons move independently from each other in a common potential, that is, a mean-field potential generated as a consequence of the interaction among nucleons (see e.g., Bohr and Mottelson 1969 Ring and Schuck 1980). They consist of a small number of protons and neutrons, collectively called nucleons. Atomic nuclei are located at the center of atoms and carry almost all the fraction of the mass of atoms.

Periodic table atomic number