  Using a Thomas-Fermi model, we calculate the structure of the electrosphere
of the quark antimatter nuggets postulated to comprise much of the dark matter.
This provides a single self-consistent density profile from ultrarelativistic
densities to the nonrelativistic Boltzmann regime that use to present
microscopically justified calculations of several properties of the nuggets,
including their net charge, and the ratio of MeV to 511 keV emissions from
electron annihilation. We find that the calculated parameters agree with
previous phenomenological estimates based on the observational supposition that
the nuggets are a source of several unexplained diffuse emissions from the
Galaxy. As no phenomenological parameters are required to describe these
observations, the calculation provides another nontrivial verification of the
dark-matter proposal. The structure of the electrosphere is quite general and
will also be valid at the surface of strange-quark stars, should they exist.
