Band terminations and maximum spin values with up to 18 aligned particles (and holes) in the Z,N=50 to 82 shells

Observed rotational bands that terminate or appear to terminate at very high spin are analyzed within the configuration constrained cranked Nilsson-Strutinsky (unpaired CNS or CNSB with pairing) formalism. Spin values for the nuclei discussed reach or come close to the maximum spin that can be built within the $Z,N=50–82$ shells. Configurations are distinguished not only by the number of particles in high-$j$ and low-$j$ shells within each $\mathcal{N}$ shell but, in some cases, also by the number of particles in pseudospin partners like $d_{5/2}{g}_{7/2}$ and $s_{1/2}{d}_{3/2}$. Configurations in ${}^{156}\mathrm{Dy}$ and ${}^{164}\mathrm{Hf}$, which terminate at $I\approx 60$, are well understood in terms of their occupation of open $j$ shells or groups of $j$ shells. The bands in ${}^{156}\mathrm{Dy}$ are tentatively observed up to termination while the bands in ${}^{164}\mathrm{Hf}$ are still a few spin units away. These terminating states are built with up to 18 aligned particles or 18 $\text{particles}+\text{holes}$ outside a core. The core is built from nucleons in filled $j$ shells, which gives no contribution to the spin. Analysis of the high-spin bands in ${}^{125,126}\mathrm{Xe}$ and ${}^{131,132}\mathrm{Ce}$ suggests that bands in ${}^{126}\mathrm{Xe}$ and ${}^{132}\mathrm{Ce}$ are observed to terminate at similar spin values, where terminating bands in ${}^{126}\mathrm{Xe}$ are observed high above yrast. It is remarkable that the deformed mean field, plus single-particle configurations, is able to provide such a comprehensive description of known experimental levels in nuclei up to spin $60\hslash$ and beyond. It is also impressive that the model can relate alignments of single-particle spin vectors to changes in shape with the nuclear spin.