Two neutrino double- $\beta$ decay of $94 \leq A \leq 150$ nuclei for the $0^{+} \rightarrow 2^{+}$ transition.

Within the PHFB approach, the $ 0^{+}\rightarrow 2^{+}$ transition of two neutrino double- $ \beta$ decay of Zr, Mo, Ru, Pd, Te and Nd isotopes is studied employing wave functions generated with four different parametrizations of the pairing plus multipole type of two-nucleon interaction and the summation method. In comparison to the $ 0^{+}\rightarrow 0^{+}$ transition, the nuclear transition matrix elements $ M_{2\nu} (2^{+})$ are quite sensitive to the deformation of the yrast 2 state. Consideration of the available theoretical and experimental results suggests that the observation of the $ 0^{+}\rightarrow 2^{+}$ transition of $ 2\nu \beta^{-} \beta^{-}$ decay may be possible in Zr, Mo, Te and Nd isotopes. The effect of deformation on the $ M_{2\nu} (2^{+})$ is also studied. [ABSTRACT FROM AUTHOR]