4G Model of Simplified and Approximate Formulae for Estimating Nuclear Mass Radii and Charge Radii

Precise determination of nuclear radii and charge radii is a cornerstone of nuclear physics, essential for understanding nuclear structure, reaction dynamics, and astrophysical phenomena. Traditional empirical models often include numerous corrections to address isotopic asymmetry, shell effects, and pairing energies, resulting in complex formulae with many fitted parameters that restrict practical use. Building on the 4G model of final unification, this work introduces a simplified, physically motivated nuclear radius framework. It separately accounts for proton and neutron contributions based on their cubic root form and incorporates an adjustable mass distribution coefficient (Cmd), empirically dependent on the fine structure ratio and the strong coupling constant. Crucially, the mass radius is formulated as the product of (Cmd) and the nuclear charge radius—a feature that directly relates unified scaling parameters to experimentally accessible quantities. Close to the stable mass numbers of Z = (2 to 118), Cmd = (1.127 to 1.382). It needs fine tuning. This novel approach’s predictive performance is rigorously benchmarked against advanced formulae incorporating detailed nuclear structure corrections. Results show that this minimalistic method achieves accuracy comparable to complex models across a broad range of nuclei while substantially reducing computational complexity. It thus provides an efficient and physically transparent tool for rapid nuclear radius estimation, suitable for both theoretical studies and practical nuclear science applications