Spin distribution of nuclear levels using the static path approximation with the random-phase approximation

We present a thermal and quantum-mechanical treatment of nuclear rotation using the formalism of the static path approximation plus the random-phase approximation. Naive perturbation theory fails because of the presence of zero-frequency modes resulting from dynamical symmetry breaking. Such modes lead to infrared divergences. We show that composite zero-frequency excitations are properly treated within the collective coordinate method. The resulting perturbation theory is free from infrared divergences. Without the assumption of individual random spin vectors, we derive microscopically the spin distribution of the level density. The moment of inertia is thereby related to the spin-cutoff parameter in the usual way. Explicit calculations are performed for ⁵⁶Fe; various thermal properties are discussed. In particular, we demonstrate that the increase of the moment of inertia with increasing temperature is correlated with the suppression of pairing correlations.