  It is well known that the ultra-relativistic Thomas-Fermi equation, amply
adopted in the study of heavy nuclei, admits an exact solution for a constant
proton distribution within a spherical core of radius Rc. Here exact solutions
of a generalized ultra-relativistic Thomas-Fermi equation are presented,
assuming a Wood-Saxon-like proton distribution and its further generalizations.
These solutions present an overcritical electric field close to their surface.
The variation of the electric fields as a function of the generalized
Wood-Saxon parameters are studied.
