  $\alpha$ decay is treated microscopically, where the unstable mother nucleus
and residual daughter nucleus are described using HFB wave functions, obtained
with the Skyrme effective interaction. From these wave functions the amplitude
for forming $\alpha$ particles in the mother nucleus is computed. Two different
Skyrme parametrizations with different pairing properties are compared, and we
find good agreement with experiment for relative decay rates in both cases. The
absolute values of the decay rates are under-estimated.
