The similar behavior of the B(E1) values of the recently observed 13 − odd tensor E1 isomers and the B(E2) values of the 10 + and 15 − even tensor E2 isomers in the Sn-isotopes has been understood in terms of the generalized seniority for multi-j orbits by using the quasi-spin scheme. This simple approach proves to be quite successful in explaining the measured transition probabilities and the corresponding half-lives in the high-spin isomers of the semi-magic Sn-isotopes. Hence, we show for the first time the occurrence of seniority isomers in the 13 − Sn-isomers, which decay by odd-tensor E1 transitions to the same seniority states.

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We present freshly evaluated B(E2 ↑; 0 + → 2 + ) values across the even-even Sn-isotopes which confirm the presence of an asymmetric behavior as well as a dip in the middle of the full valence space. We explain these features by using the concept of generalized seniority. The dip in the B(E2) values near 116 Sn is understood in terms of a change in the dominant orbits before and after the mid shell, which also explains the presence of asymmetric peaks in the B(E2) values.This approach helps in deciding the most active valence spaces for a given set of isotopes, and single out the most useful truncation scheme for Large Scale Shell Model (LSSM) calculations. The LSSM calculations so guided by generalized seniority are also able to reproduce the experimental data on B(E2) ↑ values quite well.

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Isomeric studies in neutron-rich nuclei are a powerful tool for exploring structure at the nuclear extremes. In this paper we discuss the systematic features of the excitation energies and transition probabilities of Sn isotopes in the region N = 50–82 and present their basic understanding in terms of generalized seniority. We further use generalized seniority as a probe to explore the neutron-rich seniority isomers in 134–138Sn, and to validate the neutron single-particle energies beyond N = 82. We show that these isomers behave as generalized seniority isomers, where the so-called anomalous behavior of the isomer in 136Sn may be naturally explained. We support these results by shell model calculations, where the latest neutron single-particle energies of the N = 82–126 region have been used, and the i13/2 neutron single-particle energy has been suitably modified in the renormalized charge-dependent Bonn interaction. This entails a possible new subshell closure at N = 112 due to the suggested higher location of the i13/2 neutron orbital, also consistent with the choice of orbitals in the generalized seniority scheme. However, a small reduction in the f7/2 two-body matrix elements is still required in the shell model calculations to consistently reproduce the experimental level energies as well as the transition probabilities in 134–138Sn isotopes.

Recent observation of the 6+ seniority isomers and measurements of the B(E2) values in the 134−138 Sn isotopes lying close to the neutron drip line have raised some questions about the validity of the currently used effective interactions in the neutron-rich region. Simpson et al . [Phys. Rev. Lett. 113, 132502 (2014)] had to modify the diagonal and non-diagonal νf 2 7/2 two body matrix elements of the "V lk" interaction by ∼ 150 keV in their shell model calculations in order to explain the data of 136 Sn. In contrast, we are able to explain the observed energy levels and the B(E2) values after marginal reduction of the same set of matrix elements by 25 keV in the "RCDB" (Renormalized CD-Bonn) interaction. The observed mismatch in reproducing the data of 136 Sn is due to the seniority mixing. Further, we do not find it necessary to consider the core excitations, and the "RCDB" interaction seems better suited to explain the data beyond N= 82 magic number.

We have recently applied the generalized seniority approach successfully to explain the B(E1)/B(E2)/B(E3) properties of the semi-magic nuclei. In the present paper, we extend this approach to the Schmidt model as Generalized Seniority Schmidt Model and calculate the g-factors of the various seniority states in the semi-magic nuclei. We find that the magnetic moments and the g-factors do show a particle number independent behavior in multi-j configurations, as expected in the seniority scheme. The calculated results explain the experimental trends quite well. We find that the g-factors of all the seniority states arising from a given multi-j configuration for identical nucleons is equal to the g-factor of the seniority v = 1 state from that configuration. Also, the g-factors are found to be a sensitive probe for fixing the multi-j configuration, which are fully consistent with the configurations assigned to explain the B(EL) properties in our previous works. We are also able to make definite predictions for many cases.

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