On the pressure dependence of the muon spin polarization in mixtures of noble gases

In muon spin rotation (μSR) experiments, where spin‐polarized positive muons are stopped in condensed matter, three magnetically distinguishable chemical environments can be observed. That is, the Larmor frequencies associated with diamagnetic environments and two types of paramagnetic environments (muonium and radicals) can be resolved. The chemical identities of the latter two are distinct since their Larmor frequencies are distinct, whereas the chemical identities of the possible diamagnetic species are not determined by the Larmor frequency since chemical shifts can not be resolved in μSR experiments. However, two different diamagnetic species have been observed in experiments performed on mixtures of noble gases. Their distinction arises through different thermal rate constants that lead to “fast” and “slow” relaxing components of the diamagnetic signal. The pressure dependencies of the amplitudes associated with these components are related to the stopping dynamics of muons in noble gas targets. A set of coupled rate equations for muon spin dynamics, based upon quantal Boltzmann equations, have been developed to describe this process in single component gases. This theory is now extended to mixtures. In particular, the dynamics of the muon spin is generated by the muonium hyperfine interaction and by time dependent rate constants for the various chemical species that are assumed to be present, namely, muonium and three diamagnetic species. Radicals have not yet been observed in low pressure gases. The coupled quantal rate equations are solved for two models of the stopping dynamics wherein the rates are taken as square box functions of time.