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We present a thermal and quantum-mechanical treatment of nuclear rotationusing the formalism of static path approximation (SPA) plus random-phaseapproximation (RPA). Naive perturbation theory fails because of the presence ofzero-frequency modes due to dynamical symmetry breaking. Such modes lead toinfrared divergences. We show that composite zero-frequency excitations areproperly treated within the collective coordinate method. The resultingperturbation theory is free from infrared divergences. Without the assumptionof individual random spin vectors, we derive microscopically the spindistribution of the level density. The moment of inertia is thereby related tothe spin-cutoff parameter in the usual way. Explicit calculations are performedfor 56^Fe; various thermal properties are discussed. In particular, wedemonstrate that the increase of the moment of inertia with increasingtemperature is correlated with the suppression of pairing correlations.Comment: 12 pages, 8 figures, accepted for publication in Physical Review

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