The accurate determination of nuclear radius is fundamental to understanding nuclear structure and interactions. The present study conducts a comprehensive theoretical analysis of nuclear radius measurements using various nuclear structure models, including the empirical mass-number scaling model, the Hartree-Fock approach, and the relativistic mean-field (RMF) theory. These models are systematically compared against experimental nuclear radii to evaluate their predictive accuracy and assess their strengths and limitations. The study also incorporates an uncertainty analysis to quantify the reliability of theoretical predictions, employing Monte Carlo simulations and Bayesian inference techniques to refine estimations. The results reveal that while empirical models provide reasonable approximations, they lack the precision required for heavy nuclei due to the omission of interaction effects. The Hartree-Fock and RMF models incorporate nucleon-nucleon interactions and relativistic corrections, improving predictive performance, yet systematic deviations persist, particularly in neutron-rich nuclei. Comparisons with recent studies highlight the growing role of machine learning techniques in refining nuclear radius predictions, reducing uncertainty margins, and improving model accuracy. The study emphasizes the necessity for hybrid methodologies integrating empirical models, quantum mechanical calculations, and advanced computational techniques to enhance nuclear radius predictions. In addition, Figuretechnology-inspired computational techniques, including Figurescale modeling and machine learning algorithms, offer enhanced predictive capabilities by capturing complex nuclear interactions at finer scales and reducing uncertainty in nuclear radius estimation.
