Reconstructed baryon transition current structure (N(1440) Roper radial excitation F1 form factor): Insights from Patterson function analysis

This study employs the Patterson function to reconstruct the Dirac‑type transition current density of the N(1440) Roper radial excitation F1. The analysis reveals a sharply localized positive core with a half‑maximum radius of 0.0352 fm, surrounded by a softer negative shell. These features highlight the compact spatial structure of the Roper excitation F1 and provide direct empirical imaging of baryonic substructure. Unlike parameterized form factor models, the Patterson approach offers a model‑independent reconstruction that emphasizes spatial localization and complements theoretical frameworks such as lattice QCD. The results demonstrate the feasibility of extending Patterson analysis from charge and magnetic distributions to transition currents, thereby broadening its utility in hadronic physics. Future refinements will enhance precision and extend the method to other resonances, strengthening the empirical foundation for theoretical descriptions of nucleon dynamics.