The angular momentum distribution of the deformed intrinsic nuclear state

In a Hartree-Fock or Hartree-Foek-Bogoliubov calculation of a deformed intrinsic state, one obtains a distribution of angular momentum states. Using an analogy from statistical mechanics, we obtain an expression for this distribution. The concept of an average temperature for the intrinsic state is introduced, which is directly related to the rotational energy content of the intrinsic state. The relationship of this temperature to microscopic particle-hole calculations is clarified. Assuming a rotational spectrum for the ground-state band of an axially symmetric doubly even nucleus, it is demonstrated that the deduced distribution of the angular momentum states gives rise to an overlap function of the intrinsic wave function which falls off, for small angles of rotation, as a Gaussian. Finally, the Yoccoz formula for the moment of inertia is derived using classical statistical mechanics, and semiclassical corrections to it are obtained.