Muonium ground state hyperfine structure

Ultrahigh Precision Measurements on Muonium Ground State Hyperfine Structure and Muon Magnetic Moment LAMPF Proposal, November 1986, V.W. Hughes, G zu Putlitz, P.A. Souder, Spokesmen. 

Muonium has a simpler, point-like muon nucleus and recent improvements in the theory [21, 22, 23] yield results which compare favourably with measurements of the muonium ground state hyperfine structure [24, 25] at a level of 0,13 ppm, mainly determined by uncertainties in the measured muon mass. 

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. 

The very precise measurement of the ground state hyperfine structure (hfs) is described. A new successful technique for producing muonium in vacuum has been developed and possible future experiments using this technique are presented in the second part. 

The hyperfine structure interval in hydrogen is known experimentally on a level of accuracy of one part in 1012, while the theory is of only the 10 ppm level [9]. In contrast to this, the muonium hfs interval [12] is measured and calculated for the ground state with about the same precision and the crucial comparison between theory and experiment is on a level of accuracy of few parts in 107. Recoil effects are more important in muonium (the electron to nucleus mass ratio m/M is about 1/200 in muonium, while it is 1/2000 in hydrogen) and they are clearly seen experimentally. A crucial experimental problem is an accurate determination of the muon mass (magnetic moment) [12], while the theoretical problem is a calculation of fourth order corrections (a(Za)2m/M and (Za)3m/M) [11]. 

In this paper we consider the energy level diagram of the ground state of muonium in a magnetic field (Fig. 1). The transition frequencies zv12 and 34 have been measured [5] with high precision and used to determine the hyperfine structure interval Av and the ratio of the muon magnetic moment to the... 

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