Within the context of the relativistic mean field (RMF) approach and proton-neutron quasi-particle random phase approximation (pn-QRPA) model, the nuclear ground state parameters, the Gamow Teller (GT) strength, and the stellar weak rates for N = 60 have been analyzed. The ground-state deformation parameters ( \(\beta _2\) ), binding energies (BE), neutron separation energies (S \(_n\) ), nuclear radii (r \(_n\) ), neutron skin thickness (r \(_{np}\) ), and potential energy curves (PEC) were determined utilizing the RMF framework with density-dependent meson exchange interactions (DDME2). The computed \(\beta _2\) values, based on the RMF model and the finite range droplet model (FRDM) model, were used as free variables in the pn-QRPA framework to examine the GT strength distributions and stellar \(\beta\) decay rates. It is observed that the GT strength computed via the present recipe shows a good comparison with the existing data. Furthermore, the stellar electron emission ( \(\lambda _{\beta ^{-}}\) ) and positron capture ( \(\lambda _{pc}\) ) rates were computed for \(^{96}\) Kr, \(^{98}\) Sr, \(^{100}\) Zr, \(^{102}\) Mo, \(^{104}\) Ru, and \(^{106}\) Pd at all densities and temperatures based on two different deformation parameters. Our analysis can be significant for the simulation of stellar weak rates near N = 60 core nuclei.
