  We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD)
$\Lambda N\go nN$ of $\Lambda$ hypernuclei $^{4}_\Lambda$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 strangeness-changing
transition potential is described by the one-meson-exchange model, with
commonly used parameterization. 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. All $np$ and $nn$ spectra exhibit a series of peaks in the energy
interval 110 MeV $<E_{nN}<170$ MeV, one for each occupied shell-model state.
The IPSM-a could be a pretty fair approximation for the light $^{4}_\Lambda$He
and $^{5}_\Lambda$He hypernuclei. For the remaining, heavier, hypernuclei it is
very important, however, to take into account the spreading in strength of the
deep-hole states, and bring into play the IPSM-b approach. Notwithstanding the
nuclear model that is employed the results depend only very weakly on the
details of the dynamics involved in the decay process proper. We propose that
the IPSM is the appropriate lowest-order approximation for the theoretical
calculations of the of kinetic energy sum spectra in the NMWD. It is in
comparison to this picture that one should appraise the effects of the final
state interactions and of the two-nucleon-induced decay mode.
