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

Abstract

Within the PHFB approach, the $0^{+}\to 2^{+}$ transition of two neutrino double-$\beta$ decay of ${}^{94,96}$Zr, ${}^{100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$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 $0^{+}\to 0^{+}$ 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 suggest that the observation of the 02${}^{+}$ transition of $2\nu {\beta }^{-}{\beta }^{-}$ decay may be possible in ${}^{96}$Zr, ${}^{100}$Mo, ${}^{130}$Te and ${}^{150}$Nd isotopes. The effect of deformation on the $M_{2\nu }(2^{+})$ is also studied.