  The existence of electric fields close to their critical value
$E_c=\frac{m_e^2 c^3}{e \hbar}$ has been proved for massive cores of $10^7$ up
to $10^{57}$ nucleons using a proton distribution of constant density and a
sharp step function at its boundary. We explore the modifications of this
effect by considering a smoother density profile with a proton distribution
fulfilling a Woods--Saxon dependence. The occurrence of a critical field has
been confirmed. We discuss how the location of the maximum of the electric
field as well as its magnitude is modified by the smoother distribution.
