Reconstructed baryon transition current structure (Δ(1232) magnetic): Insights from Patterson function analysis

We reconstruct the magnetic dipole transition current of the Δ(1232) baryon using a scaling approach grounded in the Patterson function. The analysis produces a Patterson half‑maximum radius of 0.864 fm, while the corresponding half‑maximum radius of the transition current density is 0.0532 fm—smaller than the Patterson‑based upper bound. This compact, model‑independent reconstruction highlights the spatial localization of the Δ(1232) transition current and provides a new empirical perspective on nucleon structure. The results underscore the importance of further theoretical development to integrate these spatial distributions with established descriptions of baryonic dynamics.