  Single and double coincidence nucleon spectra in the $\Lambda$-hypernuclei
weak decay are evaluated and discussed using a microscopic formalism. Nuclear
matter is employed together with the local density approximation which allows
us to analyze the $^{12}_{\Lambda}C$ hypernucleus non-mesonic weak decay. Final
state interactions (FSI) are included via the first order (in the nuclear
residual interaction) terms to the RPA, where the strong residual interaction
is modelled by a Bonn potential. At this level of approximation, these FSI are
pure quantum interference terms between the primary decay $(\Lambda N \to NN)$
and $(\Lambda N \to NN \to NN)$, where the strong interaction is responsible
for the last piece in the second reaction. Also the Pauli exchange
contributions are explicitly evaluated. We show that the inclusion of Pauli
exchange terms is important. A comparison with data is made. We conclude that
the limitations in phase space in the RPA makes this approximation inadequate
to reproduce the nucleon spectra. This fact, does not allow us to draw a
definite conclusion about the importance of the interference terms.
