Nuclear moment of inertia as an indicator of the phase transition in a finite system

Abstract

The purpose of this article is to derive the analytic expression for the angular-momentum dependence ($I$ dependence) of the moment of inertia in microscopic mean-field theory for both even-even and odd-mass nuclei. Based on the constrained Hartree-Fock-Bogoliubov theory, the Coriolis antipairing effect is taken into account as the second-order perturbation to the BCS basis together with the blocking effect. Instead of integration, an asymptotic series expansion is applied to the quantity in which finiteness of the nuclear system becomes tangible in the high-spin region, where the gap parameter $\ensuremath{\Delta}$ becomes much smaller than the average single-particle level distance $d$. As a result, $\ensuremath{\Delta}$ keeps a small but finite value even for high-spin states, showing that there is no sharp phase transition in the nucleus. Analytic formulas are derived for the $I$ dependence of the moment of inertia for different regions of $\ensuremath{\Delta}\ensuremath{\ge}d/2$ and $\ensuremath{\Delta}<d/2$.