The nuclear ground-state features of waiting-point proton-rich nuclei with proton numbers ranging from 28 to 38 were examined using the relativistic mean-field (RMF) model with density-dependent meson-exchange (DDME2) interaction. The ground-state properties include quadrupole deformation parameter ( \(\beta _2\) ), binding energy ( \(E_{b}\) ), one proton (neutron) separation energy (S \(_p\) , S \(_n\) ), two proton (neutron) separation energy (S \(_{2p}\) , S \(_{2n}\) ), and neutron skin thickness ( \(R_{np}\) ). The \(\beta _{2}\) values, computed using the RMF model and another set adopted from the finite range droplet model, were later employed in the proton-neutron quasi particle random phase approximation (pn-QRPA) model as an input parameter for the analysis of \(\beta\) -decay properties, including the Gamow-Teller (GT) strength distributions, \(\beta\) -decay half-lives, and stellar \(\beta ^{+}\) /electron capture rates for proton-rich nuclei ( \(^{52}\) Ni, \(^{56}\) Zn, \(^{58}\) Zn, \(^{61}\) Ga, \(^{62}\) Ge, \(^{70}\) Kr, and \(^{76}\) Sr). The calculated stellar rates changed marginally with a change in the deformation parameter. For core density \(10^{7}\) g/cm \(^3\) ( \(10^{11}\) g/cm \(^3\) ), the computed sum of \(\beta ^+\) and electron capture rates increases up to 3 (1) orders of magnitude as the core temperature rises from 0.01 to 30 GK. Additionally, the present calculated rates were compared with earlier computations for nuclei \(^{70}\) Kr and \(^{76}\) Sr that were carried out using the independent particle model (IPM). The computed pn-QRPA (FRDM) rates are up to a factor of 5 larger than the IPM results in high temperature-density environments. The results of the present investigation may prove useful in simulating realistic nucleosynthesis models.
