The ground state properties of neutron-rich nuclei have been investigated using the Relativistic Hartree-Bogoliubov model. The density-dependent functions are utilized to compute the ground state nuclear deformation ( \(\beta _{2}\) ) and potential energy curves. Yet another set of deformations was adopted from the Finite Range Droplet Model (FRDM). We examine the effect of nuclear deformation on charge-changing transitions of selected neutron-rich nuclei. Later, the computed and adopted values of ( \(\beta _{2}\) ) were used as a free parameter in the proton-neutron quasiparticle random phase approximation (pn-QRPA) model to calculate the \(\beta \) -decay properties under terrestrial and stellar conditions. It was concluded that the \(\beta \) -decay properties of neutron-rich nuclei changed with change the values of nuclear deformation. The predicted \(\beta \) -decay half-lives using FRDM \(\beta _{2}\) are 87.27% (100%) within a factor 2 (10) with measured values. 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 the 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 calculations.
