this is a collective model of the nuclei density vs radius. it has another name Fermi-shape.

\rho(r) = \frac { \rho_0} {1+ Exp( (r - R_0)/a) }

where \rho_0 is central density, or density at r = 0. R_o is the radius of half density and a is the diffuseness. when a is large, the “tail” of the shape will be longer.

the radius is measured in unit of fm 1 fm = 10^{-15} m .

R_0 can be vary from 1 fm to 7 or 8 fm.  for 16O, it is about 2 fm. and for 208Pb, it is about 6fm .

a is more or less the same for different nuclei.

the density of nuclei can be mass density or charge density, the Woods-Saxon also gives a good approximation.

for mass density, a 10^{17} kg m^{-3} . for comparison, water density is 1 kg per meter cube.

and charge density is about 0.15 e fm^{-3} .

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