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.
Susheela et al. (Thu,) studied this question.