**3. Theoretical Approaches**

Similarly, theory activities in the 100Sn region did not lose momentum in the years since the last review [1]. Indeed, several approaches ([61,77–84]) could enlarge the treated configuration space (truncation level) and/or go to new regions of the nuclidic chart for The LSSM calculations, which helped to explain certain phenomena not clarified before and suggested experiments for future studies. These calculations use mostly realistic interactions derived from a nucleon-nucleon potential with various treatments to obtain two-body matrix elements and single-particle energies as described for example in [1,83] and references therein.

On the other hand, the comparison of those advanced calculation results to the ones with a smaller model space and empirical interactions, which are doable in the scope of this review work, can shed light on certain basic principles, which were not treated yet with large codes and computer power. For this purpose, the empirical GF [85] and SLGT [86] interactions in the *p*1/2*g*9/2 model space is used here, with single-particle level energies adjusted as given in [1], to guide the basic understanding of the underlying structure.

In the scope of this work, JUN45 interaction [78] results in the πν(*f* 5/2,*p*3/2,*p*1/2,*g*9/2) (or r3*g*) model space for high spin states are also presented in Section 4 for several *N* = 50 isotones and *N* = Z nuclei of the *g*9/2 shell. The shell-model code NuShellX [87] was used for these computations. The MHJM interaction in the π*p*1/2*g*9/2 ν*d*5/2*g*7/2*d*3/2*s*1/2*h*11/2 model space originating from [88] was successfully used in the literature to describe the structure of nuclei with Z ≤ 50 and *N* ≥ 50 [89], see e.g., [1,53,90,91]. The LSSM calculations in the e.g., [61,92,93] with the SDG interaction [22] for the πυ(*g*9/2,*d*5/2,*g*7/2,*s*1/2,*d*3/2) model space (further referred as *gds*) are described in more detaill below.

Recently, new approaches were proposed in this region of nuclei promising further success. The role of 3-body residual interactions in nuclear chains in a single j-shell is discussed within the shell model [94]. Beyond the standard shell-model approach, the 3-body interaction was considered in calculations of the energies of excited states in *N =* 50 isotones [95], which caused a significant improvement in reproducing experimental values. Furthermore, nuclear flied theory group investigated Sn isotopic chain using particle-vibration coupling [96]. The quadrupole-vibrational excitations in even–even Cd isotopes was revisited by the mean-field interacting boson model [97].

As already indicated in the introduction the ab initio methods are recently possible for this region of nuclei. The prediction of energies of excited states of nuclei in vicinity of 100Sn were very recently presented based on the particle-hole effective interaction derived from shell model couple cluster method [98].
