Exact density-potential relation for the ground state of the Be atom

The exact ground-state density n(r) of the Be atom can be generated, at least in principle, from a local one-body potential energy V(r), which must include however an appropriate contribution from exchange and correlation interactions. Here an exact relation between n(r) and this given V(r) is exhibited by making use of the density matrix variational method set up by Dawson and March for two occupied levels in a one-dimensional system.