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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 thePHFB model in conjunction with the summation method. In the first step, thereliability of the intrinsic wave functions has been established by obtainingan overall agreement between a number of theoretically calculated spectroscopicproperties and the available experimental data for $ ^{94,96}$%Zr$,^{94,96,98,100}$Mo, $^{98,100,104}$Ru, $^{104,110}$Pd and $^{110}$Cdisotopes. Subsequently, the PHFB wave functions of the above mentioned nucleiare employed to calculate the nuclear transition matrix elements $M_{2\nu}$ aswell as half-lives $T{_{1/2}^{2\nu}}$. Further, we have studied the effects ofdeformation on the $M_{2\nu}$.Comment: 25 pages, 3 figure

Two-neutrino double- β decay of 94 ⩽ A ⩽ 110 nuclei for the 0+ → 0+ transition