Nuclear charge radius ($r_{\mathrm{ch}}=\sqrt{⟨r^2{⟩}_{\mathrm{ch}}}$)

The root mean square radius of a nuclear charge distribution, referred to its center. Define its charge-weighted second moment byFor a spherical charge density with finite fourth moment, insert the Taylor series $\sin u/u=1-u^2/6+O(u^4)$ into the nuclear charge form factor:Thus a radius is a low-momentum transfer slope, not necessarily the position of a sharp edge. In this real static model,The factor of two between the slopes of $F$ and $|F{|}^2$ matters when interpreting a differential scattering cross-section. A proton charge radius is the corresponding size concept for the proton; the spatial arrangement of many nucleons introduces an additional scale in a heavier atomic nucleus.