Nonlinear Energy Self-Interaction in Nuclear Binding: Evidence from the Nuclear Rotor Atlas

The Nuclear Rotor Atlas provides a geometric framework for modeling nuclear structure in which binding energy is derived from optimized configurations of coupled rotors embedded in a structured vacuum. While this approach captures a substantial portion of nuclear binding, the resulting energies exhibit a systematic residual relative to experimental values. Initial analysis shows that this residual can be reduced by introducing a nonlinear bulk term proportional to the square of nucleon number, A². However, the physical origin of this quadratic scaling is not evident from geometric considerations alone. In this work, we demonstrate that the A² term is not fundamental, but instead acts as a proxy for a more physically meaningful quantity: the total Atlas binding energy. A systematic evaluation of candidate geometric corrections—including local overlap, finite-range halo interactions, interior shielding, and global mean-field measures—fails to reproduce the observed improvement, indicating that the dominant correction is not a function of spatial geometry. Correlation analysis reveals that A² is strongly associated with the total Atlas energy, motivating the introduction of energy-based correction terms. By replacing quadratic size scaling with linear and weakly nonlinear functions of the Atlas energy, we achieve a substantial improvement in predictive accuracy, reducing root-mean-square error by approximately a factor of two across the dataset. The resulting model indicates that the dominant missing contribution to nuclear binding arises from a nonlinear dependence on the system’s own energy. This suggests a feedback mechanism in which rotor-generated energy modifies the vacuum medium, which in turn enhances binding. The results support a reinterpretation of nuclear binding within the Rotor Framework in which geometry determines baseline structure, while nonlinear energy self-interaction governs higher-order corrections. Light nuclei are shown to represent a transitional regime in which this collective energy feedback is not yet dominant. These findings provide a data-driven foundation for incorporating nonlinear energy terms into future formulations of the Rotor Field Equation.