Spin dynamics of positive muons during cyclic charge exchange and muon slowing down time

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Abstract
Larmor precession of positive muon spins has been investigated theoretically during cyclic charge exchange where the positive muon spends considerable time as muonium. Because of the interference among the muonium hyperfine states, the coherent precession of the positive muon remains largely undisturbed during rapid cyclic charge exchange. It has been shown that the slowing down time of positive muons in the gas phase can be measured directly from the phase of the Larmor precession of the muons thermalised as muonium which can be observed by the muon spin rotation ( mu SR) technique. The average spin polarisation vector (magnitude and phase) retained in the muon in Ar after cyclic charge exchange is also calculated as a function of field and pressure based on the atomic cross sections of muons and muonium which are obtained from the existing proton and hydrogen data by a simple scaling scheme.