Simple empirical order parameter for a first-order quantum phase transition in atomic nuclei

A simple, empirical, easy-to-measure effective order parameter of a first-order phase transition in atomic nuclei is presented, namely, the ratio of the energies of the first excited 6(+) and 0(+) states, distinguishing between first- and second-order transitions, and taking on a special value in the critical region, as data in Nd-Dy show. In the large N-B limit of the interacting boson approximation model, a repeating degeneracy between alternate yrast and successive 0(+) states is found in the critical region around the line of a first-order phase transition, pointing to a possible underlying symmetry.