Magnetic Quenching of Hyperfine Depolarization of Positive Muons

Abstract

The depolarization of positive muons being slowed down in an insulating material can only be accounted for by the capture of an electron into a bound state. The ground-state muonium formed in flight can be expected to break up in a time short compared to ${10}^{\ensuremath{-}10}$ sec (the time necessary for the electron to flip the muon spin via the hyperfine interaction). The effect of an external magnetic field in locking the electron spin in its initial orientation, and thereby quenching the action of the hyperfine coupling, is a useful test of the assumption of muonium as the depolarizing mechanism. If $x$ is the magnetic field strength measured in units of 1.58 kilogauss, and $\ensuremath{\tau}$ is twice the mean life of the muonium atoms with respect to breakup, measured in units of 3.58\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}11}$ sec, then it is found that the amount of depolarization for one formation and breakup process is equal to one-half of the quantity ${(1+{\ensuremath{\tau}}^{\ensuremath{-}2}+{x}^{2})}^{\ensuremath{-}1}$. By introducing $n$, the number of times that the capture-breakup process is repeated, one has two parameters and can achieve good fits to the experimental data of Sens et al. for nuclear emulsion and fused quartz. It is pointed out that the interpretation by Sens et al. of their magnetic quenching data, also based on a two-parameter formula, is not tenable, since it depends on assuming that a certain fraction of the muons are not subject to the capture and loss process.