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

The $(��^{-}��^{-})_{0��}$ 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 $��^{-}��^{-}$ 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 $T_{1/2}^{2��}$ for the $0^{+}\to 0^{+}$ transition and the available experimental data. In the present work, we study the $(��^{-}��^{-})_{0��}$ 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 $T_{1/2}^{0��}(0^{+}\to 0^{+})$ 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 $(��^{-}��^{-})_{0��}$ 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 $(��^{-}��^{-})_{2��}$ and $(��^{-}��^{-})_{0��}$ decay.
15 pages, 1 figure