Overview of Seniority Isomers
Abstract
:1. Introduction
2. Quasi-Spin Algebra: Single-j and Multi-j
- A quasi-spin scalar if is odd.
- component of the quasi-spin vector if is even.
3. Seniority (and Generalized Seniority) Isomers: Where and Why?
4. Seniority Isomers in Various Mass Regions
4.1. Ca Isotopes
4.2. Ni Isotopes
4.3. Sn Isotopes
4.4. Pb Isotopes
4.5. N = 28 Isotones
4.6. N = 50 Isotones
4.7. N = 82 Isotones
4.8. N = 126 Isotones
4.9. Cd and Te Isotopes
4.10. Hg and Po Isotopes
4.11. N = 48 and N = 52 Isotones
4.12. N = 80 and N = 84 Isotones
4.13. N = 124 and N = 128 Isotones
5. Predictions and Open Issues
- The measurement gaps in the systematics of seniority isomers require special attention from the experimentalists, since this missing piece of information would be crucial for the theoretical developments. The presence of isomers in neutron-rich Pd and Cd, for example, strongly suggests the same isomers in more neutron-rich Ru and Mo, isotonic nuclei. Similarly, future experimental data on the isomer in neutron-rich Ru (due to two neutron holes in ) will be immensely helpful in understanding the function of pairing in such a limiting and exceedingly neutron-rich nucleus. The existence of isomers in Cd also suggests the dominance of the neutron configuration for the lower lying state. Any information on the state due to two proton holes in Cd would be equally important for assessing the competitiveness between proton and neutron two-body configurations. Similar investigation for the states in Pd would also be encouraging to understand the structural evolution.
- The particle-number independent variation of the magnetic moments for the good (generalized) seniority states can be used to predict the g-factors for the gaps in measurements. For example, the g-factor for the isomer in Ca should be in the similar order to the g-factor of the isomer in Ca. Despite the fact that the two states in Ca have different seniorities, the g-factor should be equal to neutron owing to the pure-j configuration. Similarly, the g-factor in Ni isotopes for the isomers should be comparable and, if measured, would represent the nature of the implicated neutron orbital. The same can be said for the states in Ni isotopes, which are not isomeric due to the additional and permitted decay branch. Similar would be true for the seniority isomers in medium to heavy mass nuclei such as the isomers in Sn isotopes, the isomers in Pb, and lighter Pb isotopes. The same is true for the g-factors of seniority isomers in various isotonic chains.
- If the isomers have the same origin and only differ in terms of an extra odd-particle, the g-factor of odd-A isomers will be in the same order as that of even-A isomers for a given isotopic or isotonic chain. The g-factor for the isomers in odd-A Sn isotopes, for example, would be of the same order as the isomers in even-A Sn isotopes. The same will hold true for the odd-A isomers in lighter odd-A Pb isotopes due to their similarity to the neighboring even-A isomers. Similarly, the g-factor for the and isomers in respective even-A , and odd-A , isotones should be almost equal to each other. The Schmidt value for proton is n.m., although the GSSM estimate for the mixed proton configuration is +1.27 n.m. Such future moment measurements would provide the complete understanding of a nuclear structure for these isotonic isomers.
- To address the similarities and differences in the behavior of states in Cd, Sn and Te isotopes, the Q-moment measurements in heavier Te isotopes are of current experimental interest, particularly when similar measurements for Cd and Sn isotopes are now known with great precision at the ISOLDE facility [81,115]. Since the states are found to occur quite regularly in Cd, Sn and Te isotopes for the range of , one can expect the higher seniority isomers such as , , in the Cd and Te isotopes, similar to the Sn isotopes.
- The lack of experimental data on E2 decay properties of the first states below the seniority isomers in isotones prevents a conclusion on the seniority conservation in from being established. Similarly, in other heavier mass regions, firm E2 assignments below the most-aligned seniority isomer are not yet available. The E2 properties for the states below the neutron-rich seniority isomers in Sn isotopes beyond Sn and the states below the seniority isomers in Pb isotopes beyond Pb, for example, will undoubtedly contribute to realistic and effective nuclear shell model interactions. To fully comprehend the neutron–neutron/proton–proton as well as neutron–proton two-body matrix elements, comprehensive spectroscopic information for isomers and states below isomers in two-particles/holes nuclei with respect to semi-magic nuclei such as Cd and Te isotopes, Hg and Po isotopes, , 52 isotones, , 84 isotones, , 128 isotones is necessary.
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Maheshwari, B.; Nomura, K. Overview of Seniority Isomers. Symmetry 2022, 14, 2680. https://doi.org/10.3390/sym14122680
Maheshwari B, Nomura K. Overview of Seniority Isomers. Symmetry. 2022; 14(12):2680. https://doi.org/10.3390/sym14122680
Chicago/Turabian StyleMaheshwari, Bhoomika, and Kosuke Nomura. 2022. "Overview of Seniority Isomers" Symmetry 14, no. 12: 2680. https://doi.org/10.3390/sym14122680