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X(5) is a paradigm for the structure at the critical point of a particularfirst-order phase transition for which the intrinsic energy surface has twodegenerate minima separated by a low barrier. For a finite system, we show thatthe dynamics at such a critical point can be described by an effectivedeformation determined by minimizing the energy surface after projection ontoangular momentum zero, and combined with two-level mixing. Wave functions of aparticular analytic form are used to derive estimates for energies andquadrupole rates at the critical point.Comment: 14 pages, 1 figure, 2 tables, Phys. Rev. C in pres

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