re process which determines the synthesis of nearly half of the nuclei heavier than Fe. Since the vast majority of nuclides which lie on the path of the $r$-process will not be experimentally accessible in the foreseeable future, it is important to develop microscopic nuclear structure models that can provide accurate predictions of weak-interaction rates of thousands of nuclei with large neutron to proton asymmetry. There are basically two microscopic approaches that can be employed in large-scale calculations of $\beta$-decay rates: the interacting shell model and the quasiparticle random phase approximation (QRPA). While the advantage of using the shell model is the ability to take into account the detailed structure of the $\beta$-strength function [@LM.03], the QRPA approach is based on global effective interactions and provides a systematic description of $\beta$-decay properties of arbitrarily heavy nuclei along the $r$-process path [@Bor.06]. In a recent review of modern QRPA calculations of $\beta$-decay rates for astrophysical applications [@Bor.06], Borzov has emphasized the importance of performing calculations based on self-consistent mean-field models, rather than on empirical mean-field potentials, e.g. the Woods-Saxon potential. In a self-consistent framework both the nuclear ground states, i.e. the masses which determine the possible $r$-process path, and the corresponding $\beta$-decay properties are calculated from the same energy density functional or effective nuclear interaction. This approach ensures the consistency of the nuclear structure input for astrophysical modeling, and allows reliable extrapolations of the nuclear spin-isospin response to regions of very neutron-rich nuclei.

The fully consistent proton-neutron (PN) relativistic QRPA [@VPNR.03; @Paa.04] has recently been employed in the calculation of $\beta$-decay half-lives of neutron-rich nuclei in the N$\approx$50 and N$\approx$82 regions [@NMV.05]. The model is based on the relativistic QRPA [@Paa.03], formulated in the canoni