  The nonmesonic weak decay of $\Lambda$ hypernuclei using nonrelativistic
nuclear matter is studied. As the basic building block we use the Polarization
Propagator Method developed by Oset and Salcedo.
  It is shown that the exact calculation of exchange terms is required. Using
the Local Density Approximation we evaluate the nonmesonic decay width for
$^{12}_{\Lambda}C$ and compare the result with a finite nucleus calculation,
obtaining a qualitative agreement.
