  Properties of the "electron gas" - in which conduction electrons interact by
means of Coulomb forces but ionic potentials are neglected - change
dramatically depending on the balance between kinetic energy and Coulomb
repulsion. The limits are well understood. For very weak interactions (high
density), the system behaves as a Fermi liquid, with delocalized electrons. In
contrast, in the strongly interacting limit (low density), the electrons
localize and order into a Wigner crystal phase. The physics at intermediate
densities, however, remains a subject of fundamental research. Here, we study
the intermediate-density electron gas confined to a circular disc, where the
degree of confinement can be tuned to control the density. Using accurate
quantum Monte Carlo techniques, we show that the electron-electron correlation
induced by an increase of the interaction first smoothly causes rings, and then
angular modulation, without any signature of a sharp transition in this density
range. This suggests that inhomogeneities in a confined system, which exist
even without interactions, are significantly enhanced by correlations.
