**1. Introduction and Ground-State Properties**

The *N=Z=* 50 nucleus 100Sn, with *N* being the number of neutrons and *Z* being the atomic number, is the heaviest self-conjugate and doubly-magic nucleus that remains stable with respect to heavy-particle emission and thus provides an excellent opportunity for shell-model studies. In particular, its unique placement in the chart of nuclei makes it and its neighbors the most suitable to investigate neutron–proton correlations based on the coupling of single particle states with respect to a doubly-magic-core. However, in view of these advantages, the progress on the relevant experimental information in this region is moderate in spite of enormous efforts of physicists around the globe.

It directly relates to the accessibility of these nuclei in any known production reaction and therefore also to technical accelerator developments. Recent related technical developments have a large impact on this field. The history of the approaches to investigate 100Sn was addressed in the latest review [1] where the experimental and theoretical status of the region was summarized until 2013. The purpose of this work is to report on recent developments in this region relevant for the understanding of the nuclear force.

The 100Sn ground state is expected to be bound by about 3 MeV with respect to proton emission [2], which makes its yrast states accessible to *γ*-ray spectroscopy. The proton dripline was recently predicted [3] to be at *N =* 47 for the element of tin. The first ab initio prediction for the charge radius and density distribution of 100Sn was attempted in Ref. [4]. The latest example of experimental developments to study nuclear size in this region is given in Ref. [5]. In-gas-cell laser ionization spectroscopy and extraction of magnetic moments and mean-square charge radii of light Ag isotopes was presented in Ref. [6].

The strength of the Super Gamow-Teller transition [7], *B*(*GT*) from the ground state of 100Sn, which could yield the largest value observed within the electron capture (EC) decay energy, *Q*EC, window in the whole chart of nuclei, was originally predicted in Ref. [8]. It was measured for the first time by Hinke et al. [9]. Significant progress was obtained since then as the experimental value was revisited recently [10] and discussed theoretically in [11–14]. The two experimental *B*(*GT*) values, originating from beta decay process, differ significantly.

**Citation:** Górska, M. Trends in the Structure of Nuclei near 100Sn. *Physics* **2022**, *4*, 364–382. https://doi.org/ 10.3390/physics4010024

Received: 26 November 2021 Accepted: 2 March 2022 Published: 21 March 2022

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This is mainly caused by the greatest deficiency of the beta-decay spectroscopy measurements that is the determination of *Q*EC, i.e., *Qβ,* which is needed for extraction of *B*(*GT*) value. The reason for that is a strong dependence of phase-space factor *f* on the decay energy. This calls for a high-precision mass measurement of 100Sn. Indeed, also here the progress is significant. Mass measurements in the region were recently extended [15,16], suggesting that the *QEC* of Ref. [9] to be more consistent with those new results. The mass of 100Sn itself is likely within reach very soon.

The first possible excited yrast states in 100Sn are particle-hole excitations of the closed core. No excited states of 100Sn were reported thus far, as shown in Figure 1. To address directly the structure of 100Sn itself, an extended work has been invested into calculations of both *α*-cluster formation and decay probabilities in ideal heavy *α* emitters 104Te and the 212Po for a direct comparison [16]. In this microscopic calculation of *α*-cluster formation with an improved treatment of shell structure for the core nucleus, it was found out that the effective potential is sensitive to the contributing single-particle wave functions.

Striking shell effects on the *α*-cluster formation probabilities are shown for magic numbers 50, 82 and 126 by using the same nucleon-nucleon interaction. An enhanced *α*-cluster formation probability was shown for both 104Te and 212Po as compared with their neighbors. In Ref. [17], a particular enhancement in the 100Sn region was suggested with respect to that in 208Pb. The analysis of the statistical significance of the neutron skin thickness to the symmetry energy in 132Sn and comparison to proton skin in 100Sn was performed by Muir et al. [18]. As in the first case, a clear correlation was observed for neutron skin, in the later no correlation could be deduced for 100Sn.

The nuclear structure of hole states in the region "southwest" of the shell closure at 100Sn, close to the *N* = *Z* line is dominated by the *g*9/2 intruder orbital from the *N* = 4 harmonic oscillator (HO) shell. This is well separated from the *N* = 3, *pf* orbitals, both energetically and by parity, allowing only 2*p*-2*h* excitations into the intruder orbital space. Dominated by the strong proton-neutron interaction, the 0*g*9/2 orbit gives rise to unique structural features [1] such as spin-gaps, seniority [19–21] and parity-changing isomerism [22] in addition to proton-neutron pairing correlations [23] and seniority-induced symmetries [24]. Moreover, when moving below *Z =* 45, deformation and shape coexistence of spherical and

deformed shapes start to appear. Therefore, the region "southwest" of 100Sn has become and remains, the subject of ever-increasing efforts both in experiments and theory.

The *N* = *Z* nuclei provide the best quantum laboratory to investigate the characteristics of the neutron–proton (*np*) interaction, isospin symmetry and mixing, in addition to evolution of nuclear shapes. The *N* ≈ *Z* nuclei up to the *A* = 60 mass region have been intensively investigated during the past twenty years in various laboratories around the world. Here, the nuclei have been experimentally accessible as they are located only few neutrons away from their stable isotopes. From the nuclear theory perspective, especially regarding the nuclear shell model, the *N* ≈ Z nuclei between the *A* = 40–60 mass region have been an ideal subject to study since the valence nucleons occupy primarily the *f* 7/2 orbital making the calculations feasible due to the small valence space.

Currently, experimental ground-state decay and nuclear structure data, such as the level schemes and lifetimes of excited states for the *N* ≈ Z nuclei around the *A* = 60–90 mass region, are relatively scarce. This is due to the fact that these nuclei are located further away from the line of stability, near the proton-drip line. The production cross sections of these systems in nuclear reactions are very low (tens of nb to few μb). The missing experimental data from this region is naturally required in order to scrutinize and develop theoretical models operating in larger model spaces. However, radioactive ion beams (RIB) in this region are becoming gradually available for experiments, which can be utilized in various ways to search for new physics around the *N* = *Z* line.

The evolution of nuclear shell structure in the vicinity of doubly-magic nuclei is of major importance in nuclear physics. The Sn isotopes provide a unique testing ground in this respect. The Sn isotopes represent the longest chain of semi-magic nuclei in nature, which makes them attractive for systematic investigations. How the shell structure evolves as a function of the number of protons and neutrons can be related to collective as well to single-particle effects. Unique correlation effects may be manifested at a self-conjugate shell-closure as the same spin-orbit partners for neutrons and protons reside just above and below the shell gap.

A sensitive probe for correlations of this kind is to measure transition probabilities for certain selected states. With this approach the results of large-scale shell-model (LSSM) calculations based on microscopically-derived interactions can be tested through direct comparison with experiment. The study of simple nuclear systems, with only a few nucleons outside a closed core, can thus provide insight into the underlying nucleonnucleon interaction as applied to finite nuclei.

This paper summarizes briefly the new results on the structure of excited states of nuclei in 100Sn region and is organized as follows. After the general introduction including ground-state properties, the most successful experimental methods to obtain knowledge on excited states in nuclei in the region are elaborated in Section 2. Theoretical approaches are summarized briefly in Section 3.

The focus on new results of the shell-model calculations and their comparison to the recent experimental data is put in Section 4 for three sub regions describing certain symmetries shaded in blue in Figure 1. The *N =* 50 isotones are addressed in Section 4.1.1. The progress on *N=Z* nuclear chain just below 100Sn is described in Section 4.1.2. The recent results on light Sn isotopes and selected nuclei with *N >* 50 below Sn are presented in Section 4.2. The choice of presented data from recent experimental and theoretical results is based on the author's subjective taste.
