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

TL;DR

This paper investigates the two-neutrino double-beta decay transition from 0+ to 2+ states in various isotopes using the PHFB approach, highlighting the sensitivity of nuclear matrix elements to nuclear deformation and potential observability in specific isotopes.

Contribution

It introduces a detailed study of the 0+ to 2+ transition in double-beta decay using the PHFB method with multiple interaction parametrizations, emphasizing deformation effects.

Findings

Nuclear matrix elements are sensitive to deformation of the 2+ state.

Observation of the 0+ to 2+ transition may be possible in certain isotopes.

Deformation significantly influences the decay matrix elements.

Abstract

Within the PHFB approach, the $0^{+}\rightarrow 2^{+}$ 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 $0^{+}\rightarrow 0^{+}$ 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 suggest that the observation of the 0$% ^{+}\rightarrow $2$^{+}$ 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.