Abstract
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.
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