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

The $(β ^-β ^-)_0ν$ 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 $β ^-β ^-$ 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 $T_1/2^2ν$ for the $0^+\to 0^+$ transition and the available experimental data. In the present work, we study the $(β ^-β ^-)_0ν$ 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 $T_1/2^0ν(0^+\to 0^+)$ 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 $(β ^-β ^-)_0ν$ 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 $(β ^-β ^-)_2ν$ and $(β ^-β ^-)_0ν$ decay.