  We obtain the RPA summed one-meson exchange potential between nucleons in
symmetric nuclear matter at zero temperature, from a model which includes $\rho
$, $\sigma $, $\omega $ and $\pi $ mesons. The behavior of rho mesons inside
the medium is first discussed using different schemes to extract a finite
contribution from the vacuum polarization. These schemes give qualitatively
different results for the in-medium rho mass. The results are discussed in
connection with the non-renormalizability of the model. We next study the
modified potential as density increases. In the intermediate distance range, it
is qualitatively modified by matter and vacuum effects. In the long-distance
range ($r>2$ fm), one observes the presence of oscillations, which are not
present in free-space. Features on this distance range are insensitive to the
renormalization scheme.
