Muonium spin precession

Figure 1. Muonium spin precession signal for a ZnO powder sample at 5 K. The upper plot is the raw time-domain spectrum (corrected for the muon decay) while the lower plot is the corresponding frequency spectrum. The central line corresponds to the Larmor frequency of the bare muon (ionized muonium) and the two symmetrically disposed satelhtes are associated with muonium. The dotted curve is a theoretical fit using a powder-pattern hneshape.

For the case of muonium, nonresonant spin precession in a magnetic field provides a copious source of information about its crystallographic sites and the associated unpaired electron distribution around them (see Chapter 15). Here, the concentration of muons is always too low for molecule formation, and migration to impurities and implantation defects can be kept small by the short muon lifetime and use of pure material and low temperature. 

The technique of muon spin rotation involves applying a magnetic field perpendicular to the direction of the incoming beam of muons (transverse to their spin) and monitoring the resulting precession signal via the emission of positrons that are emitted preferentially in the direction of the muon spin at the moment of its radioactive decay. For the bare muons this is simply the Larmor frequency but for muonium several frequencies are observed. In the case of a small h q)erfine constant, one can easily reach the so-called Paschen-Back regime in moderate fields and then a triplet of lines is seen in a Fourier transform of the raw data. 

Muonium has been observed in pure hydrocarbons ( ), alcohols (, 7 ), and water ( ). Because Mu reacts slowly with these pure liquids, giving observable reaction lifetimes of Mu up to 4us, they can be used as solvents to study various solutes of interest. As the free triplet Mu atom reacts with the solute its observed precession frequency is damped and a decay constant, X can be obtained. The concentration dependence of the decay constant provides second order chemical rate constants for Mu addition, abstraction, spin conversion, and oxidation-reduction reactions. When analogous hydrogen atom rate constants are available the kinetic isotope effect can also be calculated. 

The technique of muon spin rotation ( SR) is described, with examples of its application in the fields of chemistry and solid state physics. It is shown how the raw experimental data contains information about the evolution of the spin polarization of muons stopped in matter. Fourier transformation provides a means of extracting the precession frequencies characteristic of various muonic species. Some manipulation of the raw data is essential to ensure accurate representation of the frequency information, and further techniques are often used to improve the final spectrum. These are discussed, and some examples are given of their effects. This is followed by descriptions of specific applications of Fourier transform / SR in the study of the light hydrogen isotope muoniim (Mu = /i e"), muonium-substituted free radicals, and paramagnetic states of the /A in sol ids. 

Recent zero-field studies of the free in longitudinal fields have revealed new and unique information on spin glass and other systems but here we concentrate on muonium and muonium-like states in zero magnetic field. In this case, precession is not observed in the classical sense of the word but rather a modulation of the muon polarization with time. This can be most easily understood in the case of muonium itself in terms of the isotropic Hamiltonian of Equation 30. As noted above, muonium is formed via the "capture" of an electron from the stopping medium. Since the fi is longitudinally polarizedl"3 (a ) but the captured e" is not (Qg or Pq), muonium forms initially in two spin states, defined by A> = lV°e> = I 1 1> and B> = I o /3e> = 1//2 10> +... 

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