Empirical Estimation of Penetration Probability in Actinide Nuclei Using Experimental α-decay Half-Lives

Penetration probability is a fundamental concept in alpha decay ([Formula: see text]-decay), as it quantifies the likelihood of an [Formula: see text]-particle tunneling through the nuclear potential barrier, a quantum mechanical process essential for decay to occur. In this study, we analyzed experimentally available [Formula: see text]-decay half-lives of actinide nuclei within the atomic number range [Formula: see text], considering a total of 158 alpha-emitting nuclei. To describe the tunneling behavior, we proposed a semi-empirical formula for penetration probability [Formula: see text] expressed as a function of [Formula: see text], consistent with the Geiger–Nuttall (GN) law. This approach allows decay properties to be estimated using only nuclear charge and decay energy. To improve accuracy, nuclei were classified into even-even, even-odd, odd-even, and odd-odd categories, and the optimized exponent [Formula: see text] was determined separately for each group to maximize the coefficient of determination ([Formula: see text]). The resulting empirical relations reproduce experimental [Formula: see text]-decay half-lives with [Formula: see text] and [Formula: see text]-values of 0.266 and 0.871, respectively. Furthermore, we predicted [Formula: see text]-decay half-lives for unmeasured actinide isotopes and compared them with results from established semi-empirical models (UNIV, UDL, NRDX, VSS, Royer, SemFIS, Horoi, and Dong). The proposed model shows excellent agreement, providing a simple yet reliable framework for [Formula: see text]-decay half-life estimation, particularly in unpredicted isotopes in the atomic number region [Formula: see text].