Ground stare properties of the two-dimensional electron gas are studied in
the deformable jellium model. The calculations are made within the self-con
sistent Hartree-Fock approximation. The phase transition from plane wave so
lutions to the corrugated state (Wigner like transition) is analysed for tw
o different crystallographic symmetries, A comparison of the results in the
cases studied is presented. The behaviour of the energy curve is studied f
or a wide range of densities. Our calculations of the melting point are wit
hin an order of magnitude of experimental data. (C) 1999 Elsevier Science B
.V. All rights reserved.