  We present a unified treatment of nuclear density cores recovering the
classic results for neutral atoms with heavy nuclei having a mass number
$A\approx 10^2--10^6$ and extrapolating these results to massive nuclear
density cores with $A\approx(m_{\rm Planck}/m_n)^3 \sim 10^{57}$. The treatment
consists of solving the relativistic Thomas-Fermi equation describing a system
of $N_n$ neutrons, $N_p$ protons and $N_e$ electrons in beta decay equilibrium.
The $N_p$ protons are distributed at a constant density within a spherical core
of radius $R_c$. A new island of stability is found for $A > A_R =
0.039(N_p/A)^{1/2}(m_{Planck}/m_n)^3$. The Coulomb repulsion, screened by
relativistic electrons, is balanced by the gravitational self-interaction of
the core. In analogy to heavy nuclei they present, near their surface, an
overcritical electric field. The relation between $A$ and $N_p$ is generalized
to an arbitrary value of the mass number, and the phenomenological relations
for $A < 1.5\cdot 10^2$ are obtained as a limiting case.
