We consider the intrinsic stability of the vortex states of a pure Bose-Ein
stein condensate confined in a harmonic potential under the effects of a co
herent atom-atom interaction. We find that stable vortices can be supported
and vortex stability can be controlled by changing the interparticle inter
action strength. At unstable regimes, a vortex will spontaneously disintegr
ate into states with different angular momenta even without external pertur
bations, with the lifetime determined by its imaginary excitation frequenci
es. [S1050-2947(99)07602-7].