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

Abstract

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 in which the rates, taken as square box functions of time, describe the charge exchange regime wherein muonium is both formed and ionized by subsequent collisions. Two post charge exchange extensions of this model are now considered. Following the charge exchange region, in the loss model, it is assumed that the rate of muonium formation is zero while the ionization rate is not. On the other hand, the capture model assumes that the ionization rate is zero while the muonium formation rate is not. Fits are presented to the available data for argon, krypton, xenon and neon. Since argon has both diamagnetic and paramagnetic signals then independent fits to each may be compared. A single set of fitting parameters has been found which describes both signals. This single fit requires a further extension of the models. In particular, a missing fraction must be assumed! The missing fraction model is also required when fits are made to the krypton and xenon data. On the other hand, the fit to the neon data is inconclusive. This is the first suggestion that a missing fraction may exist in the pure noble gases. Such missing fractions have been well established in condensed phases.