  We develop a theoretical framework for the evaluation of the coincidence
number of pairs, $N_{nN}$, and the asymmetry parameter, $a_\Lambda$, in
nonmesonic hypernuclear decay $\Lambda N\rightarrow nN$. The primary nomesonic
weak hyperon-nucleon decay process is described through the independent
particle shell model. When the effect of the strong interactions experimented
by the two nucleons leaving the residual nucleus is included, we have in
addition to the $2p1h$ primary configuration $2p'1h'$, $3p2h$, $4p3h$,
$\cdots$, etc secondary ones. We work within the $2p'1h'$ subspace of final
states assuming a simple approach for finite nuclei based on the eikonal
approximation. An optical potential including the nucleon-nucleus isoscalar and
isovector interaction is introduced to take into account the minimum nuclear
medium effects and to describe the nucleon-nucleus dispersion process along the
outgoing path. We applied the proposed description to the calculation of the
observables in $^{5}_\Lambda He$ and $^{12}_\Lambda C$ nonmesonic decays. The
calculated results show that our treatment of FSI even considered as restricted
to a subspace of states gives a good agreement with experimental data, similar
to that ones presented by more elaborated evaluations. This indicates that the
developed theoretical scheme seems to be appropriated to include more complex
configurations. We also discuss the ground state normalization effects at the
moment of including the two-nucleon induced decay ($\Lambda NN \rightarrow
nNN$) contribution.
