The extended nuclear matter model with smooth transition surface

The existence of electric fields close to their critical value E$_{c}$=(m$_{e}$c$^3$)/(e$\hbar )$ has been proved for massive cores of 10$^{7}$ up to 10$^{57}$ nucleons using a distribution of constant nuclear 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 Wood-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.