  Using deformed shell model based on Hartree-Fock intrinsic states with
$^{70}$Zn as an example and employing two realistic effective interactions,
namely jj44b that produces deformed shape and JUN45 that generates spherical
shape, it is demonstrated that the $0\nu$ and $2\nu$ nuclear transition matrix
elements for double beta decay will reduce considerably as we go from spherical
shapes to deformed shapes. This result is further substantiated by using
$^{150}$Nd as another example.
