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

TL;DR

This paper presents a self-consistent relativistic QRPA calculation of two-neutrino double beta decay, using relativistic mean field theory and residual interactions, providing results comparable to existing models.

Contribution

It introduces a relativistic QRPA framework based on relativistic BCS mean field theory for calculating two-neutrino double beta decay matrix elements.

Findings

Results are similar to QRPA and shell model calculations.

Uses a consistent parameter set for residual interactions.

Provides a relativistic approach to double beta decay calculations.

Abstract

We perform a self-consistent relativistic QRPA (RQRPA) calculation of $2\nu\b\b$-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 ${2\nu}\b\b$ matrix elements are similar to those obtained within the QRPA and the shell model.