Neutron and proton spectra from the decay of $\Lambda$ hypernuclei

We have determined the spectra of neutrons and protons following the decay of $\Lambda$ hypernuclei through the one- and two-nucleon induced mechanisms. The momentum distributions of the primary nucleons are calculated and a Monte Carlo simulation is used to account for final state interactions. From the spectra we calculate the number of neutrons ($N_n$) and protons ($N_p$) per $\Lambda$ decay and show how the measurement of these quantities, particularly $N_p$, can lead to a determination of $\Gamma_n / \Gamma_p$, the ratio of neutron to proton induced $\Lambda$ decay. We also show that the consideration of the two-nucleon induced channel has a repercussion in the results, widening the band of allowed values of $\Gamma_n / \Gamma_p$ with respect to what is obtained neglecting this channel.