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

Abstract.

Within the PHFB approach, the $0^{+}\rightarrow 2^{+}$ transition of two neutrino double-$\beta$ decay of ^{94, 96}Zr, ¹⁰⁰Mo, ¹⁰⁴Ru, ¹¹⁰Pd, ^{128, 130}Te and ¹⁵⁰Nd 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 ⁹⁶Zr, ¹⁰⁰Mo, ¹³⁰Te and ¹⁵⁰Nd isotopes. The effect of deformation on the $M_{2\nu} (2^{+})$ is also studied.