  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.
