  Atomic nuclei can be spontaneously deformed into non-spherical shapes as
many-nucleon systems. We discuss to what extent a similar deformation takes
place in many-electron systems. To this end, we employ several many-body
methods, such as the unrestricted Hartree-Fock method, post-Hartree-Fock
methods, and the density functional theory, to compute the electron density
distribution in atoms. We show that the electron density distribution of
open-shell atoms is deformed due solely to the single-particle valence
orbitals, while the core part remains spherical. This is in contrast to atomic
nuclei, which can be deformed collectively. We qualitatively discuss the origin
for this apparent difference between atoms and nuclei by estimating the energy
change due to deformation. We find that nature of the interaction plays an
essential role for the collective deformation.
