Recent data provide evidence for coexisting phases at low energy in th
e spherical-deformed transitional nucleus Sm-152. The nature of the wa
ve functions at the spherical-deformed phase transition in nuclei is a
nalyzed within the framework of the interacting-boson model. It is sho
wn that in the U(5)-SU(3) transition, two phases coexist in a very sma
ll region of parameter space around the critical value of the control
parameter xi. The coexistence region with two minima in the potential
shrinks to zero as one moves to the U(5)-O(6) transition. Implications
for other systems are briefly mentioned. [S0031-9007(98)06839-2].