  Presented here are calculations of the distortion of the density of an
electron gas due to the electrostatic field of a proton. Several models based
upon the local density approximation (LDA) of density functional theory [linear
response theory, Kohn-Sham (KS), optimized Thomas-Fermi theory (OTF), and OTF
plus perturbation corrections] are compared with one another. These models, in
turn, are compared with available results of quantum Monte Carlo (QMC)
calculations for the same system. Comparison of the KS results with the OTF
results shows a very reasonable agreement that seems to be progressively
improvable. This provides encouragement for the application of the OTF model to
condensed phase systems. The QMC calculations of the density do not agree well
with the density functional results. The reasons for this poor agreement are
not clear. This particular system is expected to be an ideal one for
application of the LDA and, thus, the poor agreement is of fundamental
importance. The lack of detail presented in the available QMC results leads us
to conclude that the QMC calculations should be attempted again. in print:
Molec. Phys. 82, 245-261(1994)
