  A simple, empirical signature of a first order phase transition in atomic
nuclei is presented, the ratio of the energy of the 6+ level of the ground
state band to the energy of the first excited 0+ state. This ratio provides an
effective order parameter which is not only easy to measure, but also
distinguishes between first and second order phase transitions and takes on a
special value in the critical region. Data in the Nd-Dy region show these
characteristics. In addition, a repeating degeneracy between alternate yrast
states and successive excited 0+ states is found to correspond closely to the
line of a first order phase transition in the framework of the Interacting
Boson Approximation (IBA) model in the large N limit, pointing to a possible
underlying symmetry in the critical region.
