The mu + 2H -> nu + n + n, mu + 3He -> nu + 3H, mu + 3He -> nu + n + d and mu + 3He -> nu + n + n + p capture reactions are studied with various realistic potentials under full inclusion of final state interactions. Our results for the two- and three-body break-up of 3He are calculated with a variety of nucleon-nucleon potentials, among which is the AV18 potential, augmented by the Urbana~IX three-nucleon potential. Most of our results are based on the single nucleon weak current operator. As a first step, we have tested our calculation in the case of the mu + 2H -> nu + n + n and mu + 3He -> nu + 3H reactions, for which theoretical predictions obtained in a comparable framework are available. Additionally, we have been able to obtain for the first time a realistic estimate for the total rates of the muon capture reactions on 3He in the break-up channels: 544 1/s and 154 1/s for the n + d and n + n + p channels, respectively. Our results have also been compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.
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