  The decay rate of quasiparticles in quantum dots is studied through the real
time calculation of the single-particle Green function in the self-consistent
approximation. The method avoids exact diagonalization, transforming the
problem into a system of coupled non-linear integral equations which may be
solved iteratively. That allows us to study systems larger than previously
treated in the literature. Our results for the inverse participation ratio of
many-body states show that the threshold energy for the quasiparticle
disintegration is $E^\ast \sim \sqrt{g} \Delta$. The delocalization transition
is soft rather than sharp. Three different regimes as function of the effective
interaction strength may be clearly identified at high energies.
