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Register a new userA new empirical formula for {alpha}-decay half-life and decay chains of Z=120 isotopes
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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.
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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 $0.697$.
Spontaneous fission and alpha decay are the main decay modes for superheavy nuclei. The superheavy nuclei which have small alpha decay half-life compared to spontaneous fission half-life will survive fission and can be detected in the laboratory through alpha decay. We have studied the alpha decay half-life and spontaneous half-life of some superheavy elements in the atomic range Z = 100-130. Spontaneous fission half-lives of superheavy nuclei have been calculated using the phenomenological formula and the alpha decay half-lives using Viola-Seaborg-Sobiczewski formula (Sobiczewski et al. 1989), semi empirical relation of Brown (1992) and formula based on generalized liquid drop model proposed by Dasgupta-Schubert and Reyes (2007). The results are reported here.
Latest experimental and evaluated $alpha$-decay half-lives between 82$leq$Z$leq$118 have been used to modify two empirical formulas: (i) Horoi scaling law [J. Phys. G textbf{30}, 945 (2004)], and Sobiczewski formula [Acta Phys. Pol. B textbf{36}, 3095 (2005)] by adding asymmetry dependent terms ($I$ and $I^2$) and refitting of the coefficients. The results of these modified formulas are found with significant improvement while compared with other 21 formulas, and, therefore, are used to predict $alpha$-decay half-lives with more precision in the unknown superheavy region. The formula of spontaneous fission (SF) half-life proposed by Bao textit{et al.} [J. Phys. G textbf{42}, 085101 (2015)] is further modified by using ground-state shell-plus-pairing correction taken from FRDM-2012 and using latest experimental and evaluated spontaneous fission half-lives between 82$leq$Z$leq$118. Using these modified formulas, contest between $alpha$-decay and SF is probed for the nuclei within the range 112$leq$Z$leq$118 and consequently probable half-lives and decay modes are estimated. Potential decay chains of $^{286-302}$Og and $^{287-303}$119 (168$leq$N$leq$184: island of stability) are analyzed which are found in excellent agreement with available experimental data. In addition, four different machine learning models: XGBoost, Random Forest (RF), Decision Trees (DTs), and Multilayer Perceptron (MLP) neural network are used to train a predictor for $alpha$-decay and SF half-lives prediction. The prediction of decay modes using XGBoost and MLP are found in excellent agreement with available experimental decay modes along with our predictions obtained by above mentioned modified formulas.
Transfermium nuclei (101$leq$Z$leq$110) are investigated thoroughly to describe structural properties viz. deformation, radii, shapes, magicity, etc. as well as their probable decay chains. These properties are explored using relativistic mean-field (RMF) approach and compared with other theories along with available experimental data. Neutron numbers N$=$152 and 162 have come forth with a deformed shell gap whereas N$=$184 is ensured as a spherical magic number. The region with N$>$168 bears witness of the phenomenon of shape transition and shape coexistence for all the considered isotopic chains. Experimental $alpha$-decay half-lives are compared with our theoretical half-lives obtained by using various empirical/semi-empirical formulas. The recent formula proposed by Manjunatha textit{et al.}, which results best among the considered 10 formulas, is further modified by adding asymmetry dependent terms ($I$ and $I^2$). This modified Manjunatha formula is utilized to predict probable $alpha$-decay chains that are found in excellent agreement with available experimental data.
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.
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