*4.1. Nuclei below 100Sn, A* ≤ *<sup>100</sup>*

4.1.1. Even-Even *N* = 50 Isotones of the *g*9/2 Shell

The seniority quantum number υ, which counts the number of unpaired nucleons for protons and neutrons occupying the same shell-model orbital, is very useful when discussing the structure based on high-spin orbitals. Just below 100Sn, isotopes with even *Z* form a long chain of a seniority isomers, which exhibit observable decays as the *g*9/2 is well isolated from other high spin orbitals. A direct consequence of the short-range nature of the nucleon-nucleon interaction is the conservation of the seniority υ in any n-particle configuration *j <sup>n</sup>* of like particles [99].

As the mixing of states with different seniority is expected to be small, several symmetries are imposed [24,100] (and references therein), of which the constant excitation energies within the shell and symmetry against the mid shell of *B*(*E2*) values for transitions with non-changing seniority, are addressed in this Section. In Figure 3 the experimental excitation energies for the 2+–8+ levels, as well as 5<sup>−</sup> are shown with the differently-colored symbols for each spin value. The lowering of the excitation energy seen for the states with even spin values is understood mostly by the increased binding of the 0<sup>+</sup> ground-state when removing protons from 100Sn. This effect is caused by the contribution of lower shell orbitals such as *p*3/2 and *f* 5/2, becoming closer to the Fermi level.

Most of the shell-model calculations, presented for *N =* 50 isotones, can reproduce level energies relatively well, with less accuracy for the 6<sup>+</sup> and 8<sup>+</sup> states. For the GF shell-model calculation (shown with continuous lines in Figure 3), the agreement is very good (note the expanded energy scale) in the lower shell e.g., for 92Mo, which is trivial as it was used to fit the two-body matrix elements (TBME) and therefore effectively includes the contribution of lower shells. It is also understandable that there is a trend of increased level deviation of the *g*9/2<sup>n</sup> coupling towards 100Sn.

**Figure 3.** Systematics of the level energies in the *N* (number of neutrons) *=* 50 isotonic chain, for even-*Z* (atomic number) nuclei. Experimental data shown with colored symbols are taken from [101].

The energy of the 5<sup>−</sup> state in 98Cd is taken from [102]. The lines shown in corresponding colors represent theoretical level energies. Calculations were done with the NuShellX code [87] using empirical interaction GF [85], SLGT [86] in the *π*(*g*9/2*p*1/2) and realistic effective interaction JUN45 [78] in the π(*f* 5/2,*p*3/2,*p*1/2,*g*9/2) and SDG in *πυ*(*g*9/2,*d*5/2,*g*7/2,*s*1/2,*d*3/2) model spaces [92]. The values of single-particle level energies were adopted from [1]. A pure *πg*9/2<sup>n</sup> configuration explains the levels 2+–8+. The 5<sup>−</sup> states are obtained from the *πp*1/2−1*g*9/2n+1 coupling. The "EXP" denotes experimental values.

To note is that the newly-observed 5<sup>−</sup> state in 98Cd [102] completes its systematics in those nuclei build of coupling *πp*1/2−1*g*9/2n+1 and resembles the trend of increasing deviation towards the full shell. The discrepancy of the calculated 5<sup>−</sup> and 8+ states from the experimental values are almost identical, while their crossing is reproduced almost perfectly at 94Ru. For the calculations using SLGT interaction (dotted lines in Figure 3), instead, the absolute values of energies are improving with increasing *Z* towards 96Pd and worsen again for 98Cd (except the 2+ state).

The energy trend of 5− states along the shell is not reproduced, similarly as for GF interaction. While for the low-spin states the JUN45 [78] spectrum is compressed, the 6+ and 8<sup>+</sup> are rather well reproduced, improving further towards the end of the shell (dashed line). The 5<sup>−</sup> state is missed by about 200 keV, which indicates the *p*1/2 single particle evolution correction needed for those isotopes.

The SDG spectrum is generally contracted, caused by the inclusion of core excitations, but it reproduces consistently the slope of the line between 96Pd and 98Cd for which the calculation is available [92]. Moreover, the second 4+ state (not shown in the figure for clarity) is predicted only 250 keV higher than the first one, which is approximately at the same energy as the first 6<sup>+</sup> state. In contrast, the second 6<sup>+</sup> state is predicted about 400 keV above the first one, which is considerably higher than the 8+ state [92].

More relevant for the wave functions, however, is the comparison of experimental reduced transition probabilities, *B(E2)* values in *N =* 50 isotones with the calculated values. In that case, all calculations including the GF calculations, presented here, can reproduce the data rather well for the 6+ and 8<sup>+</sup> states as their wave functions are mostly not affected by other configurations; see [1,100] and references therein. The *B*(*E2*) for transition from the 6+ state in 98Cd became recently available and the accuracy of that from 8+ state was improved [56]. The lower lying yrast states, however, caused an extended discussion in recent years on seniority conservation and seniority mixing in the *g9/2* orbital; see [1,100,103] and references therein.

Particularly for the nonaligned 4<sup>+</sup> systematics in the mid shell, of which two different seniority states are predicted in close vicinity, evidence is discussed [100] for seniority breakdown due to neutron excitations across the *N =* 50 shell gap. There, the clear advantage of LSSM calculation with core excitations included is evident. An extension of the experimental data to lower *Z* for *N =* 50 isotones will be soon available [104,105] and therefore the discussion on this topic is not extended in this work.
