Muonium hyperfine structure

This value depends strongly on the correctness of the theory both for the muonium hyperfine structure and the electron magnetic anomaly. Alternatively, extracting a value for a from Avhfs instead represents a most valuable stringent consistency test for different branches of physics, which each allow to obtain a precise value of a (see Fig.3). 

At present the good agreement within two standard deviations between the fine structure constant determined from muonium hyperfine structure and the one from the electron magnetic anomaly is generally considered the best test of internal consistency of QED, as one case involves bound state QED and the other one QED of free particles. 

To compare the theory of ae with experiment, it is necessary to know the value of a, which has been measured in diverse branches of physics. Currently best values of a, with relative standard uncertainty of 1 x 10-7 or less, are those based on the quantum Hall effect [32], the ac Josephson effect [25], the neutron de Broglie wavelength [33], the muonium hyperfine structure [34,35], and an absolute optical frequency measurement of the Cesium >1 line [36] ... 

Abstract. A Dirac equation with hyperfine operator and a recoil structure that remains valid even for positronium is presented and applied to the muonium hyperfine structure to the ordern a8. 

Kinoshita T and Nio M 1994 Improved theory of the muonium hyperfine structure ,... 

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]. 

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. 

Fig. 9. The spectroscopic experiments on the hyperfine structure of muonium and the Is-2s energy interval are closely related to a precise measurement of the muon muon magnetic anomaly. The measurements put a stringent test on the internal consistency of the theory of electroweak interaction and on the set of the involved fundamental constants...

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... 

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. 

QED can be considered to be one of the most precisely tested theories in physics at present. It provides an extremely accurate description of systems such as hydrogen and helium atoms, as well as for bound-leptonic systems, for example, positronium and muonium. Remarkable agreement between theory and experiment has been achieved with respect to the determination of the hyperfine structure and the Lamb shift. The same holds true for the electronic and muonic g-factors. The free-electron g-factor is determined at present as... 

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. 

Kinoshita T 1994 Improved determination of fine structure constant based on the electron g - 2 and muonium hyperfine stracture . Conference Precision Electromagnetic Measurements Digest, WE2B-1, Boulder CO (USA), (July 1994)... 

The range of nuclei of interest in the types of studies mentioned above is extensive. Correspondingly, the range of spectroscopy is also rather broad. One has at the long wavelength end to deal with fine structure and hyperfine structure in, e.g., positronium and muonium. Also optical spectroscopy is possible for positronium, especially the recently demonstrated Doppler-free two photon absorption Is -> 2s [32], These spectral regions have been already mentioned above along with their problems in scale normalization. 

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 impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

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