Nanosecond-Scale Proton Emission from Triaxially Deformed Lu-148 Predicted with High Accuracy Qp Value via Novel Bayesian Evaluation

Abstract

The half-life of the odd-odd deformed proton emitter $^{148}$Lu is predicted to be $196_{-129}^{+420}$ ns via the Wentzel-Kramers-Brillouin (WKB) approximation, in which the potential is extracted from the triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc) and the proton decay energy $Q_{\rm p}$ is computed as 2.015(89) MeV by the Bayesian Neural Network - Beihang (BNN-BH) model for the first time. As a decisive factor, the uncertainty of $S_{\rm p}$ has been improved from 411 keV (Bayesian Machine Learning, BML) to 89 keV (BNN-BH) by taking the ensemble uncertainty into account and confining the error estimation to the neighboring nuclei. In consequence, the magnitude of the half-life's uncertainty can be reduced from 4 orders to 1 order, compared to that ($5.5_{-5.3}^{+636}$ ns) with $S_{\rm p}$ from the BML model. We also found that the range of half-life predicted by the TRHBc + WKB approach is consistent with those from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) + WKB approach, and with those from an empirical formalism with the $S_{\rm p}$ obtained with the BNN-BH model. Furthermore, the means from the above 3 ways agree well with the experimental data for $^{149}$Lu, which gives us confidence to recommend a measurement of the half-life of proton emitter $^{148}$Lu.