$2\nu$ Double Beta Decay within the Relativistic QRPA

We perform a self-consistent relativistic QRPA (RQRPA) calculation of $2\nu \text{b}\text{b}$-decay based on relativistic BCS (RBCS) mean field theory results for odd-odd intermediate nuclei ${}^{48}$Sc, ${}^{76}$As, ${}^{82}$Br, ${}^{100}$Tc, ${}^{128}$I, and ${}^{130}$I. The RBCS equations that resemble the non-relativistic ones are constructed from a Dirac-Gorkov variational functional. We use the parameter set $NL1$ for the $\sigma$, $\omega$ and $\rho$ mesons. The RQRPA equations are solved for the residual $\pi +\rho$ interaction by employing the same parameters used in the RBCS for the latter meson, and experimental values for the pion and nucleon. The RQRPA results for the $2\nu \text{b}\text{b}$ matrix elements are similar to those obtained within the QRPA and the shell model.