Reconstructed baryon transition current structure (N(1440) Roper radial excitation F2 form factor): Insights from Patterson function analysis

Through Patterson function analysis, the transition current density associated with the N(1440) Roper radial excitation F₂ form factor is reconstructed in detail. The resulting profile displays a sharply confined positive core, characterized by a half‑maximum radius of 0.0642 fm, which is enveloped by a diffuse negative shell. This dual arrangement underscores the compactness of the F₂ excitation while simultaneously revealing its layered spatial organization. Unlike the Dirac‑type F₁ distribution, the F₂ reconstruction provides a complementary perspective that emphasizes empirical imaging of baryonic substructure and highlights the methodological strength of model‑independent Patterson analysis.