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$beta$-decay properties of nuclei are investigated within the relativistic nuclear energy density functional framework by varying the temperature and density, conditions relevant to the final stages of stellar evolution. Both thermal and nuclear pairing effects are taken into account in the description of nuclear properties and in the finite temperature proton-neutron relativistic quasiparticle random-phase approximation (FT-PNRQRPA) to calculate the relevant allowed and first-forbidden transitions in the $beta$-decay. The temperature and density effects are studied on the $beta$-decay half-lives between temperatures $T = 0-1.5$ MeV, and at densities $rho Y_e = 10^7$ g/cm${}^3$ and $10^9$ g/cm${}^3$. The relevant Gamow-Teller transitions are also investigated for Ti, Fe, Cd, and Sn isotopic chains at finite temperatures. We find that the $beta$-decay half-lives increase with increasing density $rho Y_e$, whereas half-lives generally decrease with increasing temperature. It is shown that the temperature effects decrease the half-lives considerably in nuclei with longer half-lives at zero temperature, while only slight changes for nuclei with short half-lives are obtained. We also show the importance of including the de-excitation transitions in the calculation of the $beta$-decay half-lives at finite temperatures. Comparing the FT-PNQRPA results with the shell-model calculations for $pf-$shell nuclei, a reasonable agreement is obtained for the temperature dependence of $beta$-decay rates. Finally, large-scale calculations of $beta$-decay half-lives are performed at temperatures $T_9(text{K}) = 5$ and $T_9(text{K}) = 10$ and densities $rho Y_e = 10^7$ g/cm${}^3$ and $10^9$ g/cm${}^3$ for even-even nuclei in the range $8 leq Z leq 82$, relevant for astrophysical nucleosynthesis mechanisms.
In the present work we calculate the allowed $beta^-$-decay half-lives of nuclei with $Z = 20 -30$ and N $leq$ 50 systematically under the framework of the nuclear shell model. A recent study shows that some nuclei in this region belong to the island
The self-consistent proton-neutron quasiparticle random phase approximation approach is employed to calculate $beta$-decay half-lives of neutron-rich even-even nuclei with $8leqslant Z leqslant 30$. A newly proposed nonlinear point-coupling effective
Artificial neural networks are trained by a standard backpropagation learning algorithm with regularization to model and predict the systematics of -decay of heavy and superheavy nuclei. This approach to regression is implemented in two alternative m
Based on the recent data in NUBASE2012, an improved empirical formula for evaluating the $alpha$-decay half-lives is presented, in which the hindrance effect resulted from the change of the ground state spins and parities of parent and daughter nucle
The $beta$-decay half-lives of 55 neutron-rich nuclei $^{134-139}$Sn, $^{134-142}$Sb, $^{137-144}$Te, $^{140-146}$I, $^{142-148}$Xe, $^{145-151}$Cs, $^{148-153}$Ba, $^{151-155}$La were measured at the Radioactive Isotope Beam Factory (RIBF) employing