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Register a new userSystematic calculations of $alpha$-decay half-lives with an improved empirical formula
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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 nuclei is included, together with a new correction factor for nuclei near the shell closures. The calculated $alpha$-decay half-lives are found to be in better agreements with the experimental data, and the corresponding root-mean-square (rms) deviation is reduced to $0.433$ when the experimental $Q$-values are employed. Furthermore, the $Q$-values derived from different nuclear mass models are used to predict $alpha$-decay half-lives with this improved formula. It is found that the calculated half-lives are very sensitive to the $Q$-values. Remarkably, when mass predictions are improved with the radial basis function (RBF), the resulting rms deviations can be significantly reduced. With the mass prediction from the latest version of Weizs{a}cker-Skyrme (WS4) model, the rms deviation of $alpha$-decay half-lives with respect to the known data falls to $0.697$.
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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 modes: (i) construction of a statistical global model based solely on available experimental data for alpha-decay half-lives, and (ii) modeling of the {it residuals} between the predictions of state-of-the-art phenomenological model (specifically, the effective liquid-drop model (ELDM)) and experiment. Analysis of the results provide insights on the strengths and limitations of this application of machine learning (ML) to exploration of the nuclear landscape in regions beyond the valley of stability.
Experimental $alpha$-decay half-life, spin, and parity of 398 nuclei in the range 50$leq$Z$leq$118 are utilized to propose a new formula (QF) with only 4 coefficients as well as to modify the Tagepera-Nurmia formula with just 3 coefficients (MTNF) by employing nonlinear regressions. These formulas, based on reduced mass ($mu$) and angular momentum taken away by the $alpha$-particle, are ascertained very effective for both favoured and unfavoured $alpha$-decay in addition to their excellent match with all (Z, N) combinations of experimental $alpha$-decay half-lives. After comparing with similar other empirical formulas of $alpha$-decay half-life, QF and MTNF formulas are purported with accuracy, minimum uncertainty and deviation, dependency on least number of fitted coefficients together with less sensitivity to the uncertainties of $Q$-values. The QF formula is applied to predict $alpha$-decay half-lives for 724 favoured and 635 unfavoured transitions having experimentally known $Q$-values. Moreover, these available $Q$-values are also employed to test various theoretical approaches viz. RMF, FRDM, WS4, RCHB, etc. along with machine learning method XGBoost for determining theoretical $Q$-values, incisively. Thereafter, using $Q$-values from the most precise theoretical treatment mentioned above along with the proposed formulas, probable $alpha$-decay chains for Z$=$120 isotopes are identified.
$beta$-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.
New recent experimental $alpha$ decay half-lives have been compared with the results obtained from previously proposed formulas depending only on the mass and charge numbers of the $alpha$ emitter and the Q$alpha$ value. For the heaviest nuclei they are also compared with calculations using the Density-Dependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulas. The correct agreement allows us to make predictions for the $alpha$ decay half-lives of other still unknown superheavy nuclei from these analytic formulas using the extrapolated Q$alpha$ of G. Audi, A. H. Wapstra, and C. Thibault [Nucl. Phys. A729, 337 (2003)].
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 of inversion. We perform calculation for $fp$ shell nuclei using KB3G effective interaction. In the case of Ni, Cu, and Zn, we used JUN45 effective interaction. Theoretical results of $Q$ values, half-lives, excitation energies, log$ft$ values, and branching fractions are discussed and compared with the experimental data. In the Ni region, we also compared our calculated results with recent experimental data [Z. Y. Xu {it et al.}, emph{Phys. Rev. Lett.} textbf{113}, 032505, 2014]. Present results agree with the experimental data of half-lives in comparison to QRPA.
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