Thermodynamic inequalities for nuclear rotation

The strictly reversible, thermodynamically equilibrium nature of the free rotation of a body makes it possible to obtain a number of bounds on the rotational characteristics within individual rotational bands of nonspherical nuclei. As a result, the bounds between which the possible values of the critical spin $J_c$ lie can be expressed exclusively in terms of a restricted number of the experimentally most accessible data on the lower phase $J<J_c$ for a given nuclide. The bounds are tested on the ground-state rotational bands (yrast lines) of even-even nuclei, in which the corresponding phase transition (backbending) has already been observed experimentally. For nuclei with pronounced non-sphericity, all the bounds are invariably confirmed. For the ground-state rotational bands for which the phase transition point $J =J_c$ has not yet been reached, predictions are made for the corresponding values of $J_c^{min}$ and, especially, $J_c^{max}$. The specific features of excited rotational bands, and also the bands of odd nuclei are discussed.