Orbital and Scattering Phenomenology of a Finite-Energy Electron Core

This work develops a controlled orbital and scattering phenomenology for a finite-energy electron core using observable quantities derived from a localized numerical density distribution. The analysis introduces a collective-coordinate interpretation connecting localized internal structure with effective long-wavelength orbital dynamics and studies the resulting structural form factors in momentum space. The computed form factors exhibit stable zero crossings, oscillatory behavior, and a robust directional hierarchy under grid refinement and fixed-domain consistency tests. Benchmark comparisons further show that matching the RMS radius alone is insufficient to reproduce the full momentum-space response. The resulting framework provides a controlled phenomenological bridge between localized finite-energy density configurations, orbital-scale physics, and high-momentum scattering observables.