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The two neutrino double beta decay of 94,96 Zr, 98,100 Mo, 104 Ru and 110 Pd nuclei for 0 + → 0 + transition is studied in the PHFB model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions has been established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties and the available experimental data for 94,96 Zr, 94,96,98,100 Mo, 98,100,104 Ru, 104,110 Pd and 110 Cd isotopes. Subsequently, the PHFB wave functions of the above mentioned nuclei are employed to calculate the nuclear transition matrix elements M 2ν as well as half-lives T 2ν 1/2 . Further, we have studied the effects of deformation on the M 2ν .

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 + → 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 + → 2 + ) transition probabilities, quadrupole moments Q(2 + ), gyromagnetic factors g(2 + ) as well as half-lives T 2ν 1/2 for the 0 + → 0 + transition and the available experimental data. In the present work, we study the (β − β − ) 0ν decay for the 0 + → 0 + transition in a mechanism involving neutrino mass and extract limits on effective mass of light as well as heavy neutrinos from the observed half-lives T 0ν 1/2 (0 + → 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 such a mass mechanism is investigated. It is noticed that the deformation effect on nuclear transition matrix elements is of approximately the same magnitude in (β − β − ) 2ν and (β − β − ) 0ν decay.