  The dynamical instability of new-born neutron stars is studied by evolving
the linearized hydrodynamical equations. The neutron stars considered in this
paper are those produced by the accretion induced collapse of rigidly rotating
white dwarfs. A dynamical bar-mode (m=2) instability is observed when the ratio
of rotational kinetic energy to gravitational potential energy $\beta$ of the
neutron star is greater than the critical value $\beta_d \approx 0.25$. This
bar-mode instability leads to the emission of gravitational radiation that
could be detected by gravitational wave detectors. However, these sources are
unlikely to be detected by LIGO II interferometers if the event rate is less
than $10^{-6}$ per year per galaxy. Nevertheless, if a significant fraction of
the pre-supernova cores are rapidly rotating, there would be a substantial
number of neutron stars produced by the core collapse undergoing bar-mode
instability. This would greatly increase the chance of detecting the
gravitational radiation.
