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Single and double coincidence nucleon spectra in the $\Lambda$-hypernucleiweak decay are evaluated and discussed using a microscopic formalism. Nuclearmatter is employed together with the local density approximation which allowsus to analyze the $^{12}_{\Lambda}C$ hypernucleus non-mesonic weak decay. Finalstate interactions (FSI) are included via the first order (in the nuclearresidual interaction) terms to the RPA, where the strong residual interactionis modelled by a Bonn potential. At this level of approximation, these FSI arepure quantum interference terms between the primary decay $(\Lambda N \to NN)$and $(\Lambda N \to NN \to NN)$, where the strong interaction is responsiblefor the last piece in the second reaction. Also the Pauli exchangecontributions are explicitly evaluated. We show that the inclusion of Pauliexchange terms is important. A comparison with data is made. We conclude thatthe limitations in phase space in the RPA makes this approximation inadequateto reproduce the nucleon spectra. This fact, does not allow us to draw adefinite conclusion about the importance of the interference terms.

Quantum interference terms in nonmesonic weak decay of $\Lambda$-hypernuclei within a RPA formalism