# Role of the nuclear orientation in hot rotating nuclei

## Description

The role of the nuclear orientation in the rotation of finite-temperature nuclei is investigated theoretically with microscopic nuclear structure models. An analytic formula is derived for the dynamic inertia tensor ${\cal J}\sp{(2)}$ of a hot rotating nucleus. This formula includes both mean field and pairing effects within the cranked finite-temperature Hartree-Fock-Bogoliubov (FTHFB) formalism. The intrinsic nuclear shape can have an arbitrary orientation relative to the rotation axis and the angular momentum can be large. Special case limits of this formula are presented and discussed. The rotation of hot triaxial nuclei is studied with the finite-temperature $i\sb{13/2}$ model. This model is used with three-dimensional cranking to calculate statistical fluctuations in the orientation of the intrinsic nuclear shape relative to the rotation axis. In the zero-temperature limit, the existence of 'tilted' yeast state solutions is demonstrated for even particle number. These solutions correspond to stable uniform rotation about an axis that lies in a principal plane of the nuclear potential. The possibility of stable tilting within the extended Landau theory of hot rotating nuclei is discussed. The FTHFB equation with three-dimensional cranking is solved to calculate statistical fluctuations in the orientation of $\sp{188}$Os relative to the nuclear spin vector. The principal axis frame is defined self-consistently for each orientation by constraining the quadrupole mass tensor to be diagonal. Orientation fluctuations are also computed with the macroscopic Landau theory of hot rotating nuclei, and the Landau results compare favorably with the microscopic FTHFB calculations. The possibility of stable tilted rotation is investigated for this nucleus. However, the nuclear free energy is found to be a minimum when the spin axis coincides with a principal axis of the quadrupole shape