Study of \(\beta \)-Decay, log ft Values and Nuclear Structure Properties of Neutron-Rich Ge Nuclei

We use the relativistic mean field (RMF) model to conduct a thorough analysis of the ground-state properties of \(^{67-80}\)Ge nuclei. Binding energies and neutron skin thicknesses are computed for a total of 14 neutron-rich Ge isotopes. This study covers a comprehensive overview of the state of the art regarding the RMF model’s explanation of nuclear ground-state properties. Furthermore, we examine the log ft values of the allowed \(\beta ^\pm \) decays and electron/positron capture rates on Ge isotopes in the mass region A = 67–80. The proton-neutron quasiparticle random phase approximation (pn-QRPA) method was employed to calculate the \(\beta \) decay properties of selected Ge isotopes. The calculated log ft values show good consistency with the measured data. The predicted \(\beta \) decay half-lives are within a factor of 2 of the measured values. For high temperature and density values prevailing in the core of massive stars, the calculated pn-QRPA stellar rates are up to an order of magnitude bigger than the independent shell model rates. The findings reported in the current investigation could prove valuable for simulating the late-stage stellar evolution of massive stars.