  The two neutrino double beta decay of $ ^{94,96}$Zr$,^{98,100}$Mo$,^{104}$%
Ru and $ ^{110}$Pd nuclei for $0^{+}\to 0^{+}$ transition is studied in the
PHFB model in conjunction with the summation method. In the first step, the
reliability of the intrinsic wave functions has been established by obtaining
an overall agreement between a number of theoretically calculated spectroscopic
properties and the available experimental data for $ ^{94,96}$%
Zr$,^{94,96,98,100}$Mo, $^{98,100,104}$Ru, $^{104,110}$Pd and $^{110}$Cd
isotopes. Subsequently, the PHFB wave functions of the above mentioned nuclei
are employed to calculate the nuclear transition matrix elements $M_{2\nu}$ as
well as half-lives $T{_{1/2}^{2\nu}}$. Further, we have studied the effects of
deformation on the $M_{2\nu}$.
