Theoretical studies of collective rotations of deformed high-K isomers

• Published in: The European physical journal. ST, Special topics Vol. 233; no. 5; pp. 1047 - 1060
• Main Authors: Xu, F. R., Fu, X. M., Liang, W. Y., Meng, Z. Y.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Subjects: Atomic; Classical and Continuum Physics; Collapse; Condensed Matter Physics; Configurations; Cranking; Deformation; Earth rotation; Isomers; Materials Science; Measurement Science and Instrumentation; Molecular; Nuclear Isomers; Nuclei; Numerical analysis; Optical and Plasma Physics; Physics; Physics and Astronomy; Rare earth elements; Review; Rotational states
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-024-01092-8

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 (
β
2
,
γ
,
β
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.