  A geometrical analysis of the stability of nuclei against deformations is
presented. In particular, we use Catastrophe Theory to illustrate discontinuous
changes in the behavior of nuclei with respect to deformations as one moves in
the N - Z space. We construct a minimalistic deformation model using the
microscopic-macroscopic approach. A third-order phase transition is found in
the liquid-drop model, which translates to a complete loss of stability (using
the Fold catastrophe) when shell effects are included. The analysis is found to
explain the instability of known fissile nuclei and also justify known decay
chains of heavy nuclei.
