On the pressure dependence of the polarization of diamagnetic muons and muonium in pure noble gases: Is there a missing fraction?

The amplitudes of the signals in μSR exhibit pressure dependencies which are associated with the stopping dynamics of muonium atoms and diamagnetic muon species observed when muons are thermalized in pure noble gases. To explain this effect, a set of coupled rate equations, with time dependent rates and based upon quantal Boltzmann equations, have been developed to describe the spin dynamics for the thermalization of the two species. These, by definition positive, rates depend upon time through the translational single particle density operators associated with each species. Thus, to exactly solve the spin dynamics, the coupled kinetic Boltzmann equations for the stopping process must also be solved. Furthermore, the rate equations also contain spin dynamics generated by the muonium hyperfine interaction. It is the presence of this hyperfine interaction which leads to the loss of polarization for low pressure gases. The coupled quantal rate equations have been solved for a model of the stopping dynamics i...