Research on stability and decay properties of superheavy nuclei based on neural network method

<sec>This study aims to develop a highly accurate method of predicting α-decay energy (<i>Q</i><sub>α</sub>) of superheavy nuclei (SHN) and to identify the region of enhanced stability (the “island of stability”) based on α-decay properties. Improving the accuracy of <i>Q</i><sub>α</sub> calculations is crucial for reliably predicting α-decay half-lives, which are essential for identifying newly synthesized superheavy elements.</sec><sec>A modified liquid-drop model (LDM) formula for calculating <i>Q</i><sub>α</sub> is proposed, eliminating explicit dependence on magic numbers to improve universality. However, the initial LDM formula alone yields a high root-mean-square deviation (RMSD) of 663.5 keV compared with experimental <i>Q</i><sub>α</sub> values from the AME2016 database for 369 nuclei with <i>Z</i> ≥ 82. In order to significantly improve accuracy, a neural network (NN) method is combined with the LDM formula. For a feedforward backpropagation (BP) neural network with a 2-21-1 architecture (2 input neurons: proton number <i>Z</i> and mass number <i>A</i>; 21 hidden neurons; 1 output neuron), the correction term <inline-formula><tex-math id="M8">\begin{document}$ \text{δ}{{Q}}_{\text{α}} $\end{document}</tex-math></inline-formula> is developed. The network is trained using the Levenberg-Marquardt algorithm on a dataset of 369 nuclei (319 training, 50 validation). The final <i>Q</i><sub>α</sub> prediction is given by <inline-formula><tex-math id="M9">\begin{document}$ Q_{\text{α}} ^{{\text{NN}}} = Q_{\text{α}} ^{{\text{Eq}}{\text{. (2)}}} + \delta Q_{\text{α}} ^{} $\end{document}</tex-math></inline-formula>. The unified decay law (UDL) formula is then used to calculate α-decay half-lives (<i>T</i><sub>1/2</sub>), with and without NN correction (denoted as UDL and UDL<sup>NN</sup>). The main results obtained are listed below.</sec><sec>1) Improved <i>Q</i><sub>α</sub> accuracy: The NN correction dramatically reduces the RMSD between calculated and experimental <i>Q</i><sub>α</sub> values from 663.5 keV (LDM alone) to 89.2 keV.</sec><sec>2) Capturing shell effects: Remarkably, although there is no explicit input of nuclear shell information, the NN-corrected <i>Q</i><sub>α</sub> predictions clearly reproduce known shell structures, including the expected shell closure near <i>N</i> = 184 for superheavy nuclei. This is evident in the systematic lowering of predicted <i>Q</i><sub>α</sub> values (implying increased stability) around the predicted doubly magic nucleus <sup>298</sup>Fl (<i>Z</i> = 114, <i>N</i> = 184) and other known shell closures (e.g., <i>N</i> = 152, <i>N</i> = 162).</sec><sec>3) Half-life predictions: Using the NN-corrected <i>Q</i><sub>α</sub> in the UDL formula (UDL<sup>NN</sup>) further refines <i>T</i><sub>1/2</sub> predictions, reducing the RMSD from 0.631 (UDL alone) to 0.423. The method reliably reproduces experimental half-lives and shell-related features, such as a significant increase in <i>T</i><sub>1/2</sub> near shell closure (e.g. <i>N</i> = 126) and odd-A/odd-odd nuclei due to blocking effects.</sec><sec>4) Validation: Predictions for recently synthesized neutron-deficient uranium isotopes <sup>214,216,218</sup>U agree well with new experimental data of <i>Q</i><sub>α</sub> and <i>T</i><sub>1/2</sub>. Predictions for Fl isotopic chains also show good agreement with experimental trends.</sec><sec>5) Stability island prediction: Maps of predicted <i>Q</i><sub>α</sub> and <i>T</i><sub>1/2</sub> in the superheavy region consistently identify minimum value (indicating maximum stability) near the theoretically predicted doube magic nucleus <sup>298</sup>Fl. A potential secondary stability center near <i>Z</i> = 126 and <i>N</i> = 228 is suggested, but further verification is needed. The longest predicted region of <i>T</i><sub>1/2</sub> coincides with the <i>N</i> = 184 shell closure.</sec><sec>The conclusions drawn from the above findings are as follows. Integrating a neural network with a modified liquid-drop model formula provides a powerful and accurate method for predicting α-decay energies (<i>Q</i><sub>α</sub>) of heavy and superheavy nuclei. The NN successfully learns and corrects complex shell effects implicitly, significantly improving prediction accuracy (RMSD reduced by ~85%). By combining the UDL formula, this method yields reliable α-decay half-lives. The results strongly confirm the existence and location of the predicted “island of stability” centered on the double magic nucleus <sup>298</sup>Fl, providing valuable theoretical guidance for future experiments on the synthesis and identification of superheavy elements.</sec>