  Sufficiently high densities in Bose-Einstein condensates provide favorable
conditions for the production of ultralong-range polyatomic molecules
consisting of one Rydberg atom and a number of neutral ground state atoms. The
chemical binding properties and electronic wave functions of these exotic
molecules are investigated analytically via hybridized diatomic states. The
effects of the molecular geometry on the system's properties are studied
through comparisons of the adiabatic potential curves and electronic structures
for both symmetric and randomly configured molecular geometries. General
properties of these molecules with increasing numbers of constituent atoms and
in different geometries are presented. These polyatomic states have spectral
signatures that lead to non-Lorentzian line-profiles.
