X (5) critical-point structure in a finite system

X (5) is a paradigm for the structure at the critical point of a particular first-order phase transition for which the intrinsic energy surface has two degenerate minima separated by a low barrier. For a finite system, we show that the dynamics at such a critical point can be described by an effective deformation determined by minimizing the energy surface after projection onto angular momentum zero and combined with two-level mixing. Wave functions of a particular analytic form are used to derive estimates for energies and quadrupole rates at the critical point