= Two-parameter Fermi nuclear charge distribution
{title2=$\rho(r)=\rho_0/[1+e^{(r-c)/a}]$}
A common spherical model of a heavy <nuclear charge distribution> uses a half-density radius $c$ and surface diffuseness $a>0$. The normalization $\rho_0$ is fixed by $4\pi\int_0^\infty r^2\rho(r)\,dr=Ze$. The 90%-to-10% surface thickness is $t=4a\ln3$: solve $\rho/\rho_0=0.9$ and $0.1$ and subtract the two radii. Typical fits have an approximately constant surface thickness and a radius scaling roughly as the cube root of <mass number>. This is a spatial density model, not an assertion of a thermal <Fermi-Dirac distribution> for nuclear positions.
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