Electron irradiation effects on muonium states in silicon

Normal and anomalous muonium were studied in electron irradiated silicon. We found that the two muonium states behave very differently: For normal muonium, the relaxation rate increases if the sample is irradiated whereas it decreases for anomalous muonium. Possible explanations for these processes are discussed.     

Preliminary calculations confirming that anomalous muonium in diamond and silicon is bond-centered interstitial muonium

The model of anomalous muonium as bond-centered interstitial muonium has been examined by approximate ab-initio Hartree-Fock calculations in diamond and silicon and found to be in excellent agreement with experiment.     

Electronic structure and hyperfine interaction of muonium in semi-conductors

The Unrestricted Hartree-Fock self-consistent field cluster procedure is being utilized for first-principle investigations of the electronic structures and hyperfine interactions in normal and anomalous muonium states in semi-conductors. Our results for the total energy for the normal muonium state for a twenty-seven atom cluster in diamond, including the muonium and its neighboring atoms, show a minimum at the tetrahedral site and a maximum at the hexagonal site indicating that normal muonium is located in the tetrahedral region and avoids the hexagonal region. Using the calculated spin-density as a function of the position of muonium and carrying out averaging over the vibrational motion of the muon governed by the total energy curve obtained from our work, we have derived a muon hyperfine constant which is about 75% of that in free muonium, in good agreement with experiment. The natures of the total energy and spindensity curves permit us to draw conclusions regarding the origin of the observed trend in the hyperfine constants for normal muonium in diamond, silicon and germanium. The UHF cluster procedure is also applied to study a model of a muon in a positively charged environment for the anomalous muonium center in diamond. This model leads to a hyperfine interaction tensor with the observed feature of strong anisotropy but significantly weaker than experiment. The results obtained for this model indicate the importance for the anomalous muonium state with its relatively weak hyperfine interaction, of exchange polarization effects inherent in the UHF procedure.     

On the kinetics of anomalous muonium in silicon

The spin relaxation rate of anomalous muonium in a longitudinal magnetic field was measured in a silicon single crystal. The results are treated as the diffusion of anomalous muonium in a silicon crystal.     

The effect of radiation defects in silicon single crystal lattice on the characteristic states of the interstitial muonium atom

Radiation defects are shown experimentally to affect differently the normal and anomalous muonium states in silicon. This evidences essentially different mobilities of the two muonium states in the sample lattice.     

Temperature dependence of the hyperfine parameters of anomalous muonium in germanium

The temperature variation of the anomalous muonium hyperfine interaction in germanium has been measured between 5 and 100 K. The results show that the component perpendicular to the defect axis decreases, while the parallel component increases with increasing temperature. These effects are a result of the interaction of anomalous muonium with the germanium host phonons.Work supported by National Science Foundation Grant DMR-79-09223.     

Mu to Mu* transition in electron irradiated silicon

A transition from normal muonium (Mu) to anomalous muonium (Mu^*) is observed in electron irradiated silicon. It is suggested that the transformation is induced by the strain field of the defect and takes place some distance away from the defect. The experiment was performed at 15 K.     

Resolved nuclear hyperfine structure of muonium centres in CuCl and GaAs by means of the avoided-level-crossing technique

Avoided-level-crossing resonances from isotropic muonium centres interacting with neighbouring nuclear spins in powdered CuCl are reported. The prominent resonances have a complex multiline structure and are strongly temperature-dependent. In addition, previously unobserved resonances in single-crystal GaAs from anomalous muonium interacting with a ⁷¹Ga neighbour are presented.     

Study of condensed nitrogen by μSR method

The temperature dependences of parameters of the muon spin relaxation in liquid and crystalline nitrogen have been studied. It has been established that in condensed nitrogen there takes place a fast depolarization of muons. An anomalous behaviour of the amplitude and phase of muon precession is found in the vicinity of the orientation phase transition in solid nitrogen. It has been shown that muon spin relaxation parameters in nitrogen do not change at reduction of the oxygen impurity content from 0.7·10⁻⁴ to 10⁻⁶. The fast depolarization of muons in condensed nitrogen is apparently due to the formation of muonium atoms. To explain the phenomena observed, a model of the muonium chemical reaction is proposed. The initial phase of the muon precession has been measured as a function of the perpendicular magnetic field to determine the state of short-lived muonium in nitrogen. It has been determined that muonium in nitrogen is in an excited state. Consideration of the nuclear hyperfine interaction of muonium in condensed nitrogen makes it possible to give a qualitative explanation for the temperature dependence of the initial amplitude of the muon precession.     

Self-consistent field cluster study of hyperfine properties of normal and anomalous muonium in elemental semiconductors

Using the Unrestricted Hartree Fock (UHF) Cluster Procedure, it is shown that for the normal muonium (Mu) center, the tetrahedral site is the most favorable in the two systems diamond and silicon investigated, while for the anomalous muonium (Mu^*) center, a site displaced in the <111> direction with respect to a vacancy in a double-positively charged environment is the appropriate one for all three elemental semiconductors. Using our calculated electronic wave-functions, one is able to explain all features of the observed hyperfine properties of both centers and, in a number of cases, obtain good quantitative agreement with experiment.     

Calculations of the hyperfine parameters of bond-centered muonium in diamond

The electronic structure of hydrogen and muonium at the bond-centered site in diamond is investigated using ab initio cluster calculations. Correlation effects are accounted for by a configuration interaction expansion and by the local density approximation in the density functional approach. The hyperfine and superhyperfine parameters for anomalous muonium are determined by averaging over the spread of the muon wave function. Good agreement with experimental hyperfine parameters is found.This work has partially been supported by the Swiss National Science Foundation.     

CPT and lorentz tests with muons

Precision experiments with muons are sensitive to Planck-scale CPT and Lorentz violation that is undetectable in other tests. Existing data on the muonium ground-state hyperfine structure and on the muon anomalous magnetic moment could be analyzed to provide dimensionless figures of merit for CPT and Lorentz violation at the levels of 4x10(-21) and 10(-23).     

Comparative calculations on the hyperfine parameters of bond‐centered impurities in silicon using high‐level ab initio techniques

The electronic structure of hydrogen and muonium at the bond‐centered site (anomalous muonium) in silicon is investigated using ab initio cluster calculations. Correlation effects are accounted for by the configuration interaction method and by density functional calculations. A detailed investigation of the different functionals is presented. The calculations using configuration interaction and the different gradient corrected density functionals are in good agreement with each other. The effect of the zero point motion was included in the investigation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Vacancy associated model for anomalous muonium in diamond,silicon and germanium

Through first-principles investigations on a number of models for anomalous muonium in diamond using the Unrestricted Hartree-Fock Cluster procedure, it is demonstrated that a muonium trapped near a double-positively charged vacancy is the most viable model for this center. This model is shown to successfully explain all the observed features of the hyperfine tensors A^⇉ in diamond, silicon and germanium, namely, oblateness, opposite signs of A_│ and A_┼ in diamond and same signs for silicon and germanium, the trend in the strengths of the hyperfine tensors from diamond to germanium and the negative sign for A_┼ in diamond.     

MuSR method and tomographic-probability representation of spin states

The muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. The time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. The entanglement phenomenon of a bipartite muon–electron system is investigated, in view of the tomographic analogs of the Bell number and the positive partial transpose (PPT) criterion. Reconstruction of the muon–electron spin state as well as the total spin tomography of the composed system is discussed.     

Muonium

Muonium, the bound state of the two structureless leptons μ⁺ and e⁻, is an ideal system to test quantum electrodynamics and tiny contributions of other interactions. This paper reviews the latest state of the measurements and theories for the muonium hyper-fine structure in the ground state and the 1S–2S splitting in muonium. The results of these experiments are indispensable to interpret a more precise measurement of the anomalous magnetic moment of the muon presently underway. Furthermore, the search for muonium-antimuonium conversion is reported and discussed with respect to lepton number conservation.     

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (Mu_T) and the diamagnetic states (μ^d), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (Mu_BC) and μ^d. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muonium states in zincblende-structured compounds

The authors present a list of results of μSR experiments in materials with the diamond and zincblende structure. Besides the muonium hyperfine parameters, additional information is tabulated: the formation probability for the different muon states, the highest temperatures at which muonium states have been observed and the types of transitions found to occur between these states. The muonium hyperfine parameters show a linear rise as a function of host ionicity from Ge to GaAs to ZnSe followed by a sharp drop to CuBr.     

Some simple thoughts about the structure of anomalous muonium

The subject of this paper is anomalous muonium and the kind of model that can be given to explain its observed properties. The implications of experimental findings on a model are discussed and several possible models are suggested. No clearly superior model yet exists, in part because of a lack of theoretical studies of possible models and in part because of the lack of sufficiently definitive experiments.This work was supported by the National Science Foundation under grant number DMR-79-09223.