Baryon transition current structure (N(1440) Roper radial excitation) revisited: Insights from Patterson function analysis

Abstract

This work applies Patterson function analysis to reconstruct the spatial distribution of the N(1440) Roper radial excitation transition current using empirical form factors. By dispensing with theoretical modeling, the method yields a density profile that is sharply localized and exhibits both positive and negative components. The reconstruction reveals a dominant central peak with a half-maximum radius of 0.0373 fm, underscoring extreme compactness. Comparative evaluation against nucleons, mesons, and light nuclei demonstrates that the Roper excitation occupies the most confined position among baryon transition currents. These findings confirm that Patterson imaging provides a transparent, reproducible framework for probing hadronic and nuclear structure, extending its scope beyond charge, magnetic, and gravitational form factors to transition currents.