  We study the perturbative correction to the ground state energy eigenvalue of
a 2-dimensional dilute fermi gas with weak short-range two body repulsion. From
the structure of the energy shift we infer the presence of an induced two body
long range repulsive interaction $ {\displaystyle {1\over{r^2}} }$ among the
constituent electrons indicating a potential instability of the fermi liquid
ground state.
