The non-mesonic weak decay of Λ hypernuclei is studied using nuclear matter. We have developed a formalism which gives a microscopic interpretation of the process of emission of particles originated in this decay. More specifically, our scheme provides a unified treatment of Γ (ΛN → NN) and N N (N NN ), the Λ non-mesonic weak decay widths and the number of emitted particles (pair of particles) of kind N (NN), respectively. We have also evaluated for the first time the quantum interference terms between the n-and p-induced weak decay amplitudes. Explicit expressions for N N and N NN are shown within the ring approximation. Using the local density approximation together with the ring approximation, we report results for the decay of the 12 Λ C hypernucleus. We have obtained values for the ratio N n /N p (N nn /N np ) in the range 1.4-1.6 (0.2-0.3), where no energy threshold have been employed. The n-and p-induced interference terms modify in less than ∼ 3% these results.