One of the main open problems in the physics of $\ensuremath{\Lambda}$ hypernuclei is the lack of a sound theoretical interpretation of the large experimental values for the ratio ${\ensuremath{\Gamma}}_{n}∕{\ensuremath{\Gamma}}_{p}\ensuremath{\equiv}\ensuremath{\Gamma}(\ensuremath{\Lambda}n\ensuremath{\rightarrow}nn)∕\ensuremath{\Gamma}(\ensuremath{\Lambda}p\ensuremath{\rightarrow}np)$. To approach the problem, we have incorporated a one-meson-exchange model for the $\ensuremath{\Lambda}N\ensuremath{\rightarrow}nN$ transition in finite nuclei in an intranuclear cascade code for the calculation of single- and double-coincidence nucleon distributions corresponding to the nonmesonic weak decay of $_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ and $_{\ensuremath{\Lambda}}^{12}\mathrm{C}$. Due to the reduction of interferences, two-nucleon coincidences are expected to give a cleaner determination of ${\ensuremath{\Gamma}}_{n}∕{\ensuremath{\Gamma}}_{p}$ than single-nucleon observables. Single-nucleon distributions are found to be less sensitive to variations of ${\ensuremath{\Gamma}}_{n}∕{\ensuremath{\Gamma}}_{p}$ than double-coincidence spectra. The comparison of our results with preliminary KEK coincidence data allows us to extract a ${\ensuremath{\Gamma}}_{n}∕{\ensuremath{\Gamma}}_{p}$ ratio for $_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ of $0.39\ifmmode\pm\else\textpm\fi{}0.11$ when multinucleon induced channels are omitted.
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