  We examine the effect of nuclear deformation on the calculated $\beta$-decay
half-lives of 55 neutron-rich nuclei. The deformation values were computed
using DD-PC1 and DD-ME2 interactions in the Relativistic Hartree-Bogoliubov
model. Yet another set of deformation was adopted from the Finite Range Droplet
Model (FRDM). The model-dependent deformation values were used as a free
parameter in the proton-neutron quasiparticle random phase approximation model
to calculate the $\beta$-decay properties under terrestrial and stellar
conditions. The Gamow-Teller strength distributions, branching ratios,
half-lives and stellar weak rates of selected nuclei were later investigated.
It was concluded that the $\beta$-decay properties of neutron-rich nuclei
changed with nuclear deformation. The FRDM computed deformation values provided
the best predictions for calculated half-lives followed by the DD-ME2
functional. The terrestrial $\beta$-decay half-lives changed up to 3 orders of
magnitude and the stellar $\beta$-rates within a factor of 2 as the
neutron-rich nuclei switched their geometrical configurations. For magic number
nucleus $^{138}$Sn, the stellar rates changed substantially by more than 1
order of magnitude as the nucleus transitioned away from the spherical shape.
Our investigation might prove useful for a realistic modeling of
nucleosynthesis calculation.
