$β$-decay properties of some astrophysically important Sc-isotopes

In the late progressive stages of heavy stars, electron capture and $β^\pm$-decay are the governing processes. The weak rates are essential inputs for modeling the stages of high-mass stars before supernova explosions. As per results obtained from previous simulations, weak rates of Scandium isotopes contribute substantially in changing the lepton-to-baryon ratio ($Y_e$) of the nuclear matter in the core. In the present analysis, we report important $β^-$-decay properties of crucial Sc isotopes in an astrophysical environment with mass numbers $49 \leq A \leq 54$. The investigation includes Gamow-Teller (GT) strength distributions, terrestrial half-lives, and stellar rates of electron capture (EC) and $β^-$-decay reactions. The calculations are performed using the proton-neutron (pn) quasi-particle random phase approximation (QRPA) model over a wide temperature range ($10^7$-$3 \times 10^{10}$ K) and density range ($10^1 - 10^{11}$ g/cm$^3$). Additionally, we compare our calculated results with available experimental and theoretical data. A good agreement is observed between our calculated half-lives and experimentally measured values. Our weak $β^-$-decay and EC rates are compared with those from the Independent-Particle Model (IPM) and Large-Scale Shell Model (LSSM). At high stellar temperatures and densities, our calculated $β^-$-decay rates are smaller than those from the other models.