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

X-rays, electrons and neutrons interact differently with matter and probe different properties. X-rays detect electron density (ED). Electrons measure the electrostatic potential (ESP) of electrons and nuclei. Neutrons measure the nuclear coherent scattering length (NCSL). The differences between NCSL maps and the other maps are well known. In contrast, ED and ESP maps are tacitly expected to be similar or even identical, as evidenced by the description of micro-ED and cryo-EM maps as "densities". Here, I demonstrate that the implicit assumption of ED and ESP equivalence is wrong, but contains a grain of truth. Based on 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. Nonetheless, peak and integrated map values depend differently on atom order number and on contributions from electrons in inner and outer CM shells. ED and ESP maps also differ in the sign and relative magnitude of excess charge effects.