  After a short introduction to the nonmesonic weak decay (NMWD) $\Lambda N\go
nN$ of $\Lambda$-hypernuclei we discuss the long-standing puzzle on the ratio
$\Gamma_n/\Gamma_p$, and some recent experimental evidences that signalized
towards its final solution. Two versions of the
Independent-Particle-Shell-Model (IPSM) are employed to account for the nuclear
structure of the final residual nuclei. They are: (a) IPSM-a, where no
correlation, except for the Pauli principle, is taken into account, and (b)
IPSM-b, where the highly excited hole states are considered to be
quasi-stationary and are described by Breit-Wigner distributions, whose widths
are estimated from the experimental data. We evaluate the coincidence spectra
in $^{4}_\Lambda$He, $^{5}_\Lambda$He, $^{12}_\Lambda$C, $^{16}_\Lambda$O, and
$^{28}_\Lambda$Si, as a function of the sum of kinetic energies
$E_{nN}=E_n+E_N$ for $N=n,p$. The recent Brookhaven National Laboratory
experiment E788 on $^4_\Lambda$He, is interpreted within the IPSM . We found
that the shapes of all the spectra are basically tailored by the kinematics of
the corresponding phase space, depending very weakly on the dynamics, which is
gauged here by the one-meson-exchange-potential. In spite of the
straightforwardness of the approach a good agreement with data is achieved.
This might be an indication that the final-state-interactions and the
two-nucleon induced processes are not very important in the decay of this
hypernucleus. We have also found that the $\pi+K$ exchange potential with soft
vertex-form-factor cutoffs $(\Lambda_\pi\approx 0.7$ GeV, $\Lambda_K\approx
0.9$ GeV), is able to account simultaneously for the available experimental
data related to $\Gamma_p$ and $\Gamma_n$ for $^4_\Lambda$H, $^4_\Lambda$He,
and $^5_\Lambda$He.
