A Finite-Energy Core for the Electron: Regularity, Stability and Experimental Consistency

This work introduces a mathematically regular classical effective model of the electron based on a smooth, finite-energy core energy-density distribution. The framework resolves the classical divergence of point-charge self-energy while remaining fully consistent with the renormalised quantum-field-theoretic description of the electron at experimentally accessible scales. The model is formulated in terms of a positive, localised radial energy density satisfying strict smoothness, integrability, and variational admissibility constraints. Rigorous analysis demonstrates that the resulting electromagnetic potential is finite everywhere, including at the origin, and reproduces the Coulomb behaviour asymptotically. The associated form factor satisfies all physical requirements, including analyticity, normalisation, and monotonic decay, and converges to the point-particle limit for experimentally relevant momentum scales. Numerical stability, convergence, and perturbation tests confirm that the physical predictions are robust and insensitive to admissible variations of the energy-density profile. Atomic-potential corrections are shown to remain far below current experimental detection thresholds, ensuring consistency with precision measurements. The finite-energy core is interpreted as a structural regularisation of the effective point-like electron used in quantum field theory, providing a mathematically well-defined classical description of the electron’s self-field structure at sub-Compton scales without modifying established quantum electrodynamics predictions.