= Nuclear charge distribution
{title2=$\rho_{\mathrm{ch}}(\mathbf r)$}
A spatial <charge density> describing the <electric charge> inside an <atomic nucleus>. In a static description centered on the <nucleus>, normalize it by
$$
\int_{\mathbb R^3}\rho_{\mathrm{ch}}(\mathbf r)\,d^3r=Ze,
$$
where $Z$ is the <atomic number> and $e>0$ the <elementary charge>. A <nuclear charge distribution> is an average over a nuclear <quantum state>, rather than a photograph of immobile <protons>. Even when the average has <spherical symmetry>, individual <nucleons> need not sit on spherical shells. The <proton charge radius> and the internal <charge density> of the <neutron> also contribute: a distribution of pointlike proton centers is an approximation to a <nuclear charge distribution>, not its definition.
The experimental attraction is that an <Electron> probes <electric charge> through the <electromagnetic interaction>, without itself feeling the <nuclear force>. Varying its <momentum transfer> changes the spatial scale tested. Long wavelengths mainly constrain a <nuclear charge radius>; shorter wavelengths can distinguish a diffuse edge from a sharper one through <diffraction>. Recovering the entire <nuclear charge distribution> from a finite range of noisy scattering data remains an <inverse problem>.
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