Correlation between nuclear isospin asymmetry and $\alpha$-particle preformation probability for superheavy nuclei from a Bayesian inference

In the study of $\alpha$ decay within the superheavy nuclear region ($Z \geq 90$ and $N \geq 140$), the $\alpha$-particle preformation probability $P_{\alpha}$ serves as a crucial physical quantity linking nuclear structure to decay observables. We introduce a phenomenological model incorporating the decay energy $Q_{\alpha}$, mass number $A$, orbital angular momentum $l$, isospin asymmetry $I$, and unpaired nucleon effect. For the first time, a Bayesian inference method combined with Markov Chain Monte Carlo (MCMC) sampling has been employed to impose global constraints on the model parameters, enabling the systematic and high-precision calculation of $P_{\alpha}$. The results reveal a significant suppressing effect of isospin asymmetry on $P_{\alpha}$, a finding independently corroborated by random forest-based feature importance analysis, which identified $I$ as a dominant factor. Furthermore, calculations using the maximum a posteriori (MAP) parameters not only reproduce the shell effect at $N=152$ but also yield $\alpha$ decay half-life predictions in excellent agreement with experimental ones, thereby validating this model universality. This work provides the first global analysis tool for probing the $\alpha$ preformation mechanism in superheavy nuclei, underscores the potential of the Bayesian framework for inverting complex nuclear physics problems, and establishes a reliable theoretical benchmark for guiding future experimental exploration of superheavy nuclei.