  Radioactive decay of nuclei via emission of $\alpha$ particles has been
studied theoretically in the framework of a superasymmetric fission model using
the double folding (DF) procedure for obtaining the $\alpha$-nucleus
interaction potential. The DF nuclear potential has been obtained by folding in
the density distribution functions of the $\alpha$ nucleus and the daughter
nucleus with a realistic effective interaction. The M3Y effective interaction
has been used for calculating the nuclear interaction potential which has been
supplemented by a zero-range pseudo-potential for exchange along with the
density dependence. The nuclear microscopic $\alpha$-nucleus potential thus
obtained has been used along with the Coulomb interaction potential to
calculate the action integral within the WKB approximation. This subsequently
yields microscopic calculations for the half lives of $\alpha$ decays of
nuclei. The density dependence and the exchange effects have not been found to
be very significant. These calculations provide reasonable estimates for the
lifetimes of $\alpha$ radioactivity of nuclei.
