  An alternative approach to density functional theory based on self-consistent
field theory for ring polymers is applied to neutral atoms hydrogen to neon in
their ground states. The spontaneous emergence of atomic shell structure and
spherical symmetry-breaking of the total electron density is predicted by the
model using ideas of polymer excluded-volume between pairs of electrons to
enforce the Pauli-exclusion principle, and an exact electron self-interaction
correction. The Pauli potential is approximated and correlations are neglected,
leading to comparisons with Hartree-Fock theory, which also ignores
correlations. The model shows excellent agreement with Hartree-Fock theory for
the atomic binding energies and density profiles of the first six elements,
providing exact matches for the elements hydrogen and helium. The predicted
shell structure starts to deviate significantly past the element neon and
spherical symmetry-breaking is first predicted to occur at carbon instead of
boron. The self-consistent field theory energy functional which describes the
model is decomposed into thermodynamic components to trace the origin of
spherical symmetry-breaking. It is found to arise from the electron density
approaching closer to the nucleus in non-spherical distributions, which lowers
the energy despite resulting in frustration between the quantum kinetic energy,
electron-electron interaction, and the Pauli exclusion interaction. The
symmetry-breaking effect is also found to have minimal impact on the binding
energies. The pair density profiles display behaviour similar to polymer
macro-phase separation, where electron pairs occupy lobe-like structures that
combined together, resemble traditional electronic orbitals. It is further
shown that the predicted densities satisfy known constraints and produce the
same total electronic density profile that is predicted by quantum mechanics.
