The Woods-Saxon potential is a mean field potential for the nucleons (protons and neutrons) inside an atomic nucleus. It represent an average potential that a given nucleon feels from the forces applied on each nucleon. The parametrization is $$ \hat{u}_{\mathrm{ext}}(r)=-\frac{V_0}{1+\exp{(r-R)/a}}, $$ with \( V_0\approx 50 \) MeV representing the potential well depth, \( a\approx 0.5 \) fm length representing the "surface thickness" of the nucleus and \( R=r_0A^{1/3} \), with \( r_0=1.25 \) fm and \( A \) the number of nucleons. The value for \( r_0 \) can be extracted from a fit to data, see for example M. Kirson's article.