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Theoretical studies of collective rotations of deformed high-K isomers

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Abstract

In this article, we have reviewed our theoretical studies of collective rotations of high-K isomers in deformed nuclei. As one of methods which we have developed, the configuration-constrained total Routhian surface (CCTRS) based on a macroscopic–microscopic model has been found to be a powerful theoretical tool to describe isomers and their collective rotations. The CCTRS calculation provides a straightforward self-consistent way to determine the deformation which can change with increasing the collective rotational frequency and/or seniority of the state. To overcome the pairing collapse of numerical calculations encountered in the conventional pairing approach (e.g., BCS or Bogoliubov pairing) due to weakened pairings with unpaired nucleons in isomeric states, we have developed the CCTRS method using the particle-number-conserved (PNC) pairing approach in which the pairing is treated with the methodology of the many-body shell model. The CCTRS is calculated in a deformation lattice with the deformation parameters (\(\beta _2\), \(\gamma \), \(\beta _4\)). It is important that one should constrain the specific configuration in the CCTRS calculation, which has been achieved using the average Nilsson numbers to identify and track the single-particle orbitals specified in the intrinsic configuration of the isomer. With the CCTRS method, we have investigated many isomeric states and their rotational bands. As examples, we show in this review the calculations of collective rotational bands of isomers in rare-earth nuclei where rich data have been available. Furthermore, we have also developed a full microscopic configuration-constrained cranking model based on the Skyrme Hartree–Fock approach. Similar to the macroscopic–microscopic CCTRS, the pairing is treated by the PNC method to avoid the pairing collapse in pairing numerical calculations. As example, we show in this review the calculations of the rotational bands of \(^{178}\)W isomers.

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The isomers and their collective rotational bands of mass-170 nuclei have been investigated, where rich experimental data have been available.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grants nos. 12335007, 11835001, 11921006, 12035001. We acknowledge the High-Performance Computing Platform of Peking University for providing computational resources.

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Authors and Affiliations

  1. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing, 100871, China

    F. R. Xu, W. Y. Liang & Z. Y. Meng

  2. Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou, 516000, China

    F. R. Xu

  3. National Institute for Radiological Protection, Chinese Center for Disease Control and Prevention, Beijing, 100088, China

    X. M. Fu

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Xu, F.R., Fu, X.M., Liang, W.Y. et al. Theoretical studies of collective rotations of deformed high-K isomers. Eur. Phys. J. Spec. Top. (2024). https://doi.org/10.1140/epjs/s11734-024-01092-8

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