X-rays, electrons, and neutrons as probes of atomic matter

X-rays, electrons, and neutrons probe different properties of matter. X-rays feel electron density (ED). Electrons sense the electrostatic potential (ESP) of electrons and nuclei. Neutrons are sensitive to nuclear coherent scattering length (NCSL). While NCSL maps are widely understood to be different, ED and ESP maps are tacitly assumed to be similar. Here, I show that the belief in ED and ESP map equivalence is mistaken, but contains a grain of truth. Using density functional theory (DFT), the Bethe-Mott (BM) relation, and the Thomas-Fermi (TF) and Cromer-Mann (CM) atomic models, I show that ED and ESP maps are indeed more similar to each other than to NCSL maps. Nevertheless, peak and integrated map values depend differently on the atomic order number and on the contributions from electrons in the inner and outer CM shells. ED and ESP maps also differ in the sign and relative magnitude of excess charge effects.