Ground-State Rotor Configurations of Atomic Nuclei

Within the Rotor Dynamics Framework, nucleons are modeled as localized soliton solutions of a curvature field defined on a four-dimensional rotor vacuum manifold. Previous work established the interaction energetics of these solitons and derived a nuclear mass formula from rotor curvature energy. The present paper determines the equilibrium spatial configuration of nucleon solitons that minimizes the curvature energy functional, thereby defining the ground-state structure of atomic nuclei. By applying stationary conditions to the multi-soliton energy functional, an equilibrium separation between neighboring nucleons emerges, producing an approximately constant interior nuclear density and the observed radius scaling relation R ≈ r₀A^ (1/3). The resulting nuclear interior forms a connected curvature network in which nucleons interact primarily with nearby neighbors, naturally giving rise to saturation of nuclear binding. At the nuclear boundary this network terminates, producing a curvature deficit that generates the surface energy contribution of the nuclear mass formula. These results establish atomic nuclei as equilibrium multi-rotor configurations of the curvature field and provide the geometric foundation for subsequent analysis of collective nuclear dynamics within the rotor framework.