Nuclear Jacobi and Poincaré transitions at high spins and temperatures: Account of dynamic effects and large-amplitude motion

Abstract

We present a theoretical analysis of the competition between the so-called nuclear Jacobi and Poincar\'e shape transitions as a function of spin at high temperatures. The latter condition implies the method of choice, a realistic version of the nuclear liquid drop model, here the Lublin-Strasbourg drop model. We address specifically the fact that the Jacobi and Poincar\'e shape transitions are accompanied by the flattening of the total nuclear energy landscape as a function of the relevant deformation parameters, which enforces large-amplitude oscillation modes that need to be taken into account. For that purpose we introduce an approximate form of the collective Schr\"odinger equation whose solutions are used to calculate the most probable deformations associated with the nuclear Jacobi and Poincar\'e transitions. We discuss selected aspects of the new description focusing on the critical-spin values for both types of these transitions.