Partition functions in the dynamical symmetry limits of the interacting-boson model

In the large boson number (N) limit, analytical formulae for the partition functions are derived in the three dynamical symmetry limits (U(5), SU(3), and O(6)) of the interacting-boson model (IBM). In the U(5) limit the partition function is that of a five-dimensional oscillator and in the SU(3) limit it decomposes into rotational and vibrational parts. These are similar to the geometric-model results. In addition IBM gives an expression for O(6) nuclei; in the O(6) limit the partition function decomposes into O(6) (one-dimensional oscillator) and O(5) (γ-unstable vibration) parts. Finite-boson-number effects are studied numerically and they are found to be important for temperatures T > or ∼ 1 MeV. (orig.)