Neutron Charge Structure Revisited: Insights from Patterson Function Analysis

We apply the Patterson function to investigate the neutron’s Patterson charge density. The resulting radial profile reveals a central positive charge core, sharply peaked at the origin with a magnitude of 2.53 fm⁻⁶. The density decreases to zero at r = 0.11 fm, becomes negative, reaches a minimum of −0.097 fm⁻⁶ at r = 0.15 fm, and returns to zero at r = 0.27 fm. The radius corresponding to half-maximum of the central positive peak is 0.05 fm. The neutron’s charge distribution can be reconstructed by deconvoluting the Patterson charge density, under the constraint that the total charge is zero (see Eq. (1) of Yuen, Unpublished 1). According to Kaiser and Weise (2024), the nucleon consists of a compact core of valence quarks (~0.5 fm) surrounded by a meson cloud (~1 fm). While the Patterson-derived structure may also feature a twolayered profile, the 0.05 fm half-maximum radius is an order of magnitude smaller than the conventional quark-core size, suggesting a more compact central charge concentration than typically assumed.