  The behavior of the self diffusion constant of Langevin particles interacting
via a pairwise interaction is considered. The diffusion constant is calculated
approximately within a perturbation theory in the potential strength about the
bare diffusion constant. It is shown how this expansion leads to a systematic
double expansion in the inverse temperature $\beta$ and the particle density
$\rho$. The one-loop diagrams in this expansion can be summed exactly and we
show that this result is exact in the limit of small $\beta$ and $\rho\beta$
constant. The one-loop result can also be re-summed using a
semi-phenomenological renormalization group method which has proved useful in
the study of diffusion in random media. In certain cases the renormalization
group calculation predicts the existence of a diverging relaxation time
signalled by the vanishing of the diffusion constant -- possible forms of
divergence coming from this approximation are discussed. Finally, at a more
quantitative level, the results are compared with numerical simulations, in
two-dimensions, of particles interacting via a soft potential recently used to
model the interaction between coiled polymers.
