Shape effects on double beta decay of $^{70}$Zn and $^{150}$Nd in deformed shell model

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.