Particle-number conserving analysis of the high-spin structure of $^{159}$Ho

The high-spin rotational bands in odd-$Z$ nuclei $^{159}$Ho ($Z=67$) are investigated using the cranked shell model with the pairing correlations treated by a particle-number conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency $\hbar\omega$ are reproduced very well by the calculations. The splitting between the signature partners of the yrast band $7/2^-[523]$ is discussed and the splitting of the excited band $7/2^+[404]$ above $\hbar\omega \sim 0.30$~MeV is predicted due to the level crossing with $1/2^+[411]$. The calculated $B(E2)$ transition probabilities are also suggested for future experiments.