Nuclear deformation and neutrinoless double-$\beta$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd nuclei in mass mechanism

Abstract

The $({\beta }^{-}{\beta }^{-}{)}_{0\nu }$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd isotopes for the $0^{+}\to 0^{+}$ transition is studied in the Projected Hartree-Fock-Bogoliubov framework. In our earlier work, the reliability of HFB intrinsic wave functions participating in the ${\beta }^{-}{\beta }^{-}$ decay of the above mentioned nuclei has been established by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$, gyromagnetic factors $g(2^{+})$ as well as half-lives $T_{1/2}^{2\nu }$ for the $0^{+}\to 0^{+}$ transition and the available experimental data. In the present work, we study the $({\beta }^{-}{\beta }^{-}{)}_{0\nu }$ decay for the $0^{+}\to 0^{+}$ transition in the mass mechanism and extract limits on effective mass of light as well as heavy neutrinos from the observed half-lives $T_{1/2}^{0\nu }(0^{+}\to 0^{+})$ using nuclear transition matrix elements calculated with the same set of wave functions. Further, the effect of deformation on the nuclear transition matrix elements required to study the $({\beta }^{-}{\beta }^{-}{)}_{0\nu }$ decay in the mass mechanism is investigated. It is noticed that the deformation effect on nuclear transition matrix elements is of approximately same magnitude in $({\beta }^{-}{\beta }^{-}{)}_{2\nu }$ and $({\beta }^{-}{\beta }^{-}{)}_{0\nu }$ decay.

arXiv comment15 pages, 1 figure

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