Candidates for three-quasiparticle $K$-isomers in odd-even Md-Rg nuclei

Abstract

We performed a search for three-quasiparticle high-$K$ isomer candidates in odd-even Md - Rg nuclei by considering the lowest lying 1$\pi$2$\nu$ and 3$\pi$ excitations. Our approach involves calculating the energies of different nuclear configurations using a microscopic-macroscopic model with the Woods-Saxon potential. We explore three pairing scenarios: blocking, quasi-particle BCS method, and particle number projection formalism. The optimal deformations for both ground-states and high-$K$ configurations are determined through a four-dimensional energy minimization process. By analyzing the obtained excitation energies, we discuss the most promising candidates for high-$K$ isomers and compare them, where possible, with existing experimental data. We also discuss a possible isomer $\alpha$-decay hindrance using calculated $Q_{\alpha}$-hindrances.