Nuclear Transition Matrix Elements for Double-β Decay Within PHFB Model

Employing the projected-Hartree-Fock-Bogoliubov (PHFB) approach, nuclear transition matrix elements (NTMEs) have been calculated to study the three complementary modes of $\beta ^{-}\beta ^{-}$ decay, namely two neutrino $% \beta ^{-}\beta ^{-}$ (2$\nu \beta ^{-}\beta ^{-}$) decay, neutrinoless $% \beta ^{-}\beta ^{-}$ (0$\nu \beta ^{-}\beta ^{-}$) decay within mass mechanism and Majoron accompanied 0$\nu \beta ^{-}\beta ^{-}$ (0$\nu \beta ^{-}\beta ^{-}\chi $) decay. Reliability of HFB wave functions generated with four different parametrizations of the pairing plus multipolar type of effective two-body interaction has been ascertained by comparing a number of nuclear observables with the available experimental data. Specifically, the calculated NTMEs $M^{(2\nu )}$ of 2$\nu \beta ^{-}\beta ^{-}$ decay have been compared with the observed data. Effects due to different parametrizations of effective two-body interactions, form factors and short-range correlations have been studied. It has also been observed that deformation plays a crucial role in the nuclear structure aspects of 0$\nu \beta ^{-}\beta ^{-}$ decay. Uncertainties in NTMEs calculated with wave functions generated with four different parametrizations of the pairing plus multipolar type of effective two-body interaction, dipole form factor and three different parametrizations of Jastrow type of short-range correlations within mechanisms involving light Majorana neutrinos, heavy Majorona neutrinos, sterile neutrinos and Majorons have been statistically estimated.