Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

Abstract

We study systematically the evolutive behaviors of some energy ratios, E2 transition rate ratios and isomer shift in the nuclear shape phase transitions. We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition, similar to that in the second order phase transition.