Muon-Electron Muonium Like System

Consider the case of an isotropic, static (or time averaged) hyperfine interaction between the muon and the electron, that is represented by the following Hamiltonian, which includes the Zeeman energy terms of the electron and the muon. 

Cox [11] has discussed the relaxation mechanisms in this type of system in detail with experimental results and simulations to clearly demonstrate the various aspects. The most likely candidate that would account for the relaxation due to molecular dynamics is shown to be the fluctuation of the hyperfine interaction or the so called Fermi contact term. The hyperfine constant is in fact a thermal average over the different vibrational modes of the molecule. Therefore the molecular vibrations or librations will modulate the hyperfine constant. Hyperfine interaction is in general anisotropic, except in the gas or liquid state when the fast molecular tumbling averages out the anisotropy leaving the isotropic part. One can think of two separate mechanisms of relaxation depending on the modulation of either the isotropic part or the anisotropic part. 

Cox [11] has also shown that, even though the xSR response is in principle a superposition of several exponential terms, in practice they appear in combinations such that, whenever the eigenvalues differ greatly in magnitude, only one of these has significant weight. Alternatively, when the different eigenvalues have 

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Abstract. Muonium is a hydrogen-like system which in many respects may be viewed as an ideal atom. Due to the close confinement of the bound state of the two pointlike leptons it can serve as a test object for Quantum Electrodynamics. The nature of the muon as a heavy copy of the electron can be verified. Furthermore, searches for additional, yet unknown interactions between leptons can be carried out. Recently completed experimental projects cover the ground state hyperfine structure, the ls-2s energy interval, a search for spontaneous conversion of muonium into antimuonium and a test of CPT and Lorentz invariance. Precision experiments allow the extraction of accurate values for the electromagnetic fine structure constant, the muon magnetic moment and the muon mass. Most stringent limits on speculative models beyond the standard theory have been set. 

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> +... 

Figure 7.4 Breit-Rabi energy level diagram for a muonium like (or a muoniated radical) system. is the muon-electron hyperflne constant and Ws is the total quantum number.

In the following section new results on muonium spectroscopy are presented. Muonium (y e ) is a hydrogen-like atom consisting of two leptons. It provides an ideal system to determine muon properties and measure muon-electron interactions. is one of... 

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