  We apply the quantum Singwi-Tosi-Land-Sjolander (QSTLS) theory for a study of
many-body effects in the quasi-two-dimensional (Q2D) electron liquid (EL) in
GaAs/AlxGa1-xAs heterojunctions. The effect of the layer thickness is included
through a variational approach. We have calculated the density, spin-density
static structure factors, spin-dependent pair distribution functions (PDF) and
compared our results with those of two-dimensional (2D) EL given in earlier
papers. Using the static structure factors (SSF) we have calculated various
dynamic correlation functions such as spin-dependent local-field factors (LFF)
and effective potentials of the Q2D EL. We have also calculated the inverse
static dielectric function of the 2D and Q2D EL using different approximations.
We find that the effect of finite thickness on the dielectric function is
remarkable and at the intermediate values of wave number q there is a
significant difference between the QSTLS and STLS results.
