$K$-isomeric states in the isotopic and isotonic chains of $^{178}$Hf

TL;DR

This paper investigates the structure and formation of $K$-isomeric states in $^{178}$Hf using a self-consistent Skyrme Hartree-Fock-BCS approach, identifying regions where specific configurations contribute to isomerism.

Contribution

It applies a self-consistent SHFBCS method with SIII interaction to analyze $K$-isomers in $^{178}$Hf, extending previous approaches to this mass region.

Findings

Identifies proton and neutron configurations responsible for $K$-isomer formation.

Tests the applicability of the Skyrme SIII interaction in deformed nuclei.

Outlines the limits of the SHFBCS approach in describing $K$-isomers.

Abstract

We study the evolution of $K^{\pi}=6^{+}$ and $8^{-}$ two-quasiparticle (q.p.) configurations in the isotopic and isotonic chains of even-even deformed nuclei around $^{178}$Hf and their ability to describe series of observed $K$-isomer excitations within the framework of a Skyrme Hartree--Fock--BCS (SHFBCS) approach using SIII interaction and seniority pairing strengths with self-consistent blocking. We apply the approach along the prescription in [Phys. Rev. C {\bf 105}, 044329 (2022)] used to describe $K$-isomers in the actinide and transfermium mass regions. The calculations allow us to identify the regions where proton or neutron configurations or their mixture may be responsible for the $K$-isomer formation. The obtained results provide a detailed test for the Skyrme SIII interaction used and outline the limits of applicability of the overall SHFBCS approach in the regions of well deformed nuclei. The study suggests that similar systematic analysis can be implemented in the heavier mass regions whenever enough data are available.