  We use the thread model for linear chains of interacting monomers, and the
``polymer reference interaction site model'' (PRISM) formalism to determine the
monomer-monomer pair correlation function $h_{mm}(r)$ for dilute and
semi-dilute polymer solutions, over a range of temperatures from very high
(where the chains behave as self-avoiding walks) to below the $\theta$
temperature, where phase separation sets in. An inversion procedure, based on
the HNC integral equation, is used to extract the effective pair potential
between ``average'' monomers on different chains. An accurate relation between
$h_{mm}(r)$, $h_{cc}(r)$ [the pair correlation function between the polymer
centers of mass (c.m.)], and the intramolecular form factors is then used to
determine $h_{cc}(r)$, and subsequently extract the effective c.m.-c.m. pair
potential $v_{cc}(r)$ by a similar inversion procedure. $v_{cc}(r)$ depends on
temperature and polymer concentration, and the predicted variations are in
reasonable agreement with recent simulation data, except at very high
temperatures, and below the $\theta$ temperature.
