  Based on the relativistic mean field theory and the Thomas-Fermi
approximation, we study the surface properties of compressed, superheavy atoms.
By compressed, superheavy atom we mean an atom composed by a superheavy nuclear
core (superheavy nucleus) with mass number of the order of $10^4$, and
degenerate electrons that neutralize the system. Some electrons penetrate into
the superheavy nuclear core and the rest surround it up to a distance that
depends upon the compression level. Taking into account the strong, weak, and
electromagnetic interactions, we numerically study the structure of compressed,
superheavy atoms and calculate the nuclear surface tension and Coulomb energy.
We analyze the influence of the electron component and the background matter on
the nuclear surface tension and Coulomb energy of compressed, superheavy atoms.
We also compare and contrast these results in the case of compressed,
superheavy atoms with phenomenological results in nuclear physics and the
results of the core-crust interface of neutron stars with global charge
neutrality. Based on the numerical results we study the instability against
Bohr-Wheeler surface deformations in the case of compressed, superheavy atoms.
The results in this article show the possibility of the existence of such
compressed, superheavy atoms, and provide the evidence of strong effects of the
electromagnetic interaction and electrons on the structure of compressed,
superheavy atoms.
