  Nuclear matrix elements (NMEs) for two-neutrino double-beta decay
($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy
density functional (REDF). The properties of nuclei involved in the decay are
obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and
relevant nuclear transitions are described using the relativistic
proton-neutron quasiparticle random phase approximation based on relativistic
energy density functional (REDF-QRPA). Three effective interactions have been
employed, including density-dependent meson-exchange (DD-ME2) and point
coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are
described consistently both in $T=1$ and $T=0$ channels using a separable
pairing interaction. The optimal values of $T=0$ pairing strength parameter
$V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives.
The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several
nuclides experimentally known to undergo this kind of decay: $^{48}$Ca,
$^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe,
$^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the
NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained
using optimal values of $V_{0pp}$ are discussed in comparison to previous
studies. The results of the present work represent an important benchmark for
the future applications of the relativistic framework in studies of
neutrinoless double-beta decay.
