The high-spin rotational states of ${}_{}{}^{162}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{174}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ are calculated microscopically by diagonalizing the cranking Hamiltonian $H-\omega J_x$ using both BCS and fully particle-number projected wave functions. The computational effort in the latter case is greatly reduced due to a newly derived compact formula for the residuum integral. The results show that pairing collapse does not occur in all four nuclei up to spin 20. The moderate increase of the moment of inertia at low spin is due to both higher-order cranking and Coriolis-antipairing effects. The crossing of the decoupled two-quasiparticle band with the ground band is responsible for the rapid increase of the moment of inertia at high spin. The present calculations are able to produce the rotational energies fairly well in general, but the Nilsson single-particle levels have to be adjusted in order to reproduce the backbending behavior in ${}_{}{}^{162}{}_{}{}^{}\mathrm{Er}$.

NUCLEAR STRUCTURE Calculated high-spin rotational states by diagonalizing cranking model. New formula for particle-number projection. $g_R$ factor, backbending, Coriolis-antipairing, and rotational alignment effects.

• Received 28 March 1977

DOI:https://doi.org/10.1103/PhysRevC.16.1179