In this section, we make use of the Monte Carlo simulations to understand our data and extract the physics. The details of our Monte Carlo code SMC has been already given in Section 5.1. The physics input into the simulations is mostly taken from the Nuclear Atlas [16,17] for scattering cross sections, and Faifman et al. for the resonant [133,70,71,72] and nonresonant  molecular formation rates, with exceptions that (a) the muon transfer rate in , s-1, and formation rate (nonresonant) s-1 were taken from our measurements using the same data set , and (b) the low energy behavior of Faifman's resonant formation rate was modified to reflect the recent measurement  and theory ; the rate in at meV was set to 130 s-1. This set of physics input parameters will be referred to as the nominal input to the simulations. Our experimental data will confront these physics cross sections and rates.