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.     

Muon spin rotation studies at SIN

Recently the accelerator and the muon channel at SIN became operational. We report here on some of the first positive muon spin rotation experiments at SIN. The first experiment we discuss concerns the chemistry of muonium. We have observed for the first time a muonium or radical signal in pure water. Next, we discuss the application of the positive muon for the study of ferromagnetic metals and alloys. First measurements on a single crystal of iron around liquid helium temperature seem to indicate that at low temperature the muon does not diffuse. We further report on the first stroboscopic observation of the muon spin rotation which will allow one to take full advantage of the high stopping density at SIN.     

Electronic structure, dynamics, and metastability of muonium in semiconductors

Muonium centers are light hydrogen-like centers formed when positive muons are stopped in crystalline semiconductors. Detailed information on the hyperfine structure, dynamics and metastability of muonium are obtained using a combination of muon spin rotation or relaxation, muon level-crossing resonance and related methods. The expected close similarity to hydrogen, especially with regard to electronic structure, is important since the equivalent information on isolated hydrogen is either less detailed or completely absent. There are also interesting differences between muonium and hydrogen. In particular muonium dynamics are expected to exhibit enhanced quantum mechanical effects since the muon has only 1/9th the proton mass. In this paper we review the current status of experiments.     

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.     

Radiofrequency muon depolarization in the muonium + nuclear spin system

The effect of a considerable strengthening of muon depolarization in ALC resonance experiments was predicted for the muonium + nuclear spin system in the presence of a radiofrequency field. A mathematical approach was developed for obtaining analytic solutions that described the muon spin dynamics in ALC experiments, including a particular exact solution that contained much information about the system studied in fairly low magnetic radiofrequency fields. An analysis of these solutions and numerical calculations allowed us to comprehensively analyze muon depolarization patterns in a radiofrequency field. The results reveal the potential of muon depolarization strengthening for considerably increasing the sensitivity of experimental studies of muonium interactions with neighboring nuclear spins and for obtaining new spectroscopic information.     

Observation of “decoupled” diamagnetic muon states in Alkali halides by muon spin resonance

The states of positive muons in KCl, NaCl and KI were studied with the muon spin resonance method under a 3 kG decoupling longitudinal field, revealing a considerably larger fraction of diamagnetic muon state than observed by the conventional spin rotation method. The origin of this fraction, which increases with temperature, is attributed to a muonium to muon transition in solids.     

Muonium to diamagnetic muon conversion in KCl and NaCl revealed by time-differential muon spin resonance

The conversion of muonium into a diamagnetic muon state in KCl and NaCl was directly observed by detecting a time-delayed appearance of diamagnetic muon states with muon spin resonance. The conversion rate, determined from the time-differential resonance signals, shows a thermal activation characteristic in temperature variation.     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Charge exchange of muons in gases: Experimental implications from rate theory

The effects of the charge exchange process on muon spin dynamics have been investigated using a density operator formalism with special interest placed upon the diamagnetic muon and paramagnetic muonium signals observed after thermalization. In the charge exchange region the dynamics of the spin density operator is assumed to be determined by the muonium hyperfine interaction and by electron capture and loss processes for muons. Analytical expressions are obtained for the amplitudes and phases of the diamagnetic muon and paramagnetic muonium signals as a function of the duration of the charge exchange region,t _c, which is inversely proportional to the number density of the moderating gas. The theoretical signals exhibit three features which have, as yet, to be experimentally observed, namely: (i) that the amplitudes associated with the muonium Larmor frequency and with the hyperfine frequency are not, in general, equal, (ii) that all the amplitudes are, in general, damped oscillatory functions oft _c (temperature/pressure) and (iii) that phase jumps occur when an amplitude decreases to zero and then increases with falling pressure. Fits to the experimental argon data are discussed in light of the above points.     

Test of CPT and Lorentz invariance from muonium spectroscopy

Following a suggestion from Kostelecky et al., we evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts deltanu(12) and deltanu(34) to nu(12) and nu(34), the two transitions involving muon spin flip, which were precisely measured in ground state muonium in a strong magnetic field of 1.7 T. The shifts would be indicated by anticorrelated oscillations in nu(12) and nu(34) at the Earth's sidereal frequency. No time dependence was found in nu(12) or nu(34) at the level of 20 Hz, limiting the size of some CPT and Lorentz-violating parameters at the level of 2x10(-23) GeV.     

Spin relaxation studies of the muonium substituted ethyl radical in the gas phase

This short communication draws attention to the power of μSR and related measurements in providing an unusually complete characterisation of muonium substituted organic radicals in the gas phase. Spectroscopic information is available from muon spin rotation and muon level crossing resonance, giving all the nuclear hyperfine coupling constants, just as in the liquid phase. In addition, measurements of the relaxation time of the muon Zeeman energy become possible; these are potentially informative on the molecular collision dynamics. Demonstration results are presented in summary for the muonium substituted ethyl radical, ĊH₂CH₂Mu, in ethene gas.     

Precise measurement of hfs constant of the muonium substituted radical in cis-polyacetylene

The state of the muon in cis-polyacetylene was studied by muon spin rotation method under high transverse magnetic field. The most of the muons are found to be in muonium substituted radical state. The hyperfine coupling constant was determined to be 91 MHz with a line width of 10 MHz.     

Muon-spin-rotation study of muon polarization losses in plastic scintillators and quartz

Muon polarization losses in plastic scintillators of two types and in fused quartz have been studied by the μSR method. The muon and muonium spin precession spectra have been measured on the μSR setup placed at the output of the muon channel of the Gatchina synchrocyclotron. It has been shown that a significant fraction of stopped muons participate in the formation of the muonium. As a result, these muons lose their polarization completely. The magnitude of muon depolarization depends considerably on the type of plastic. It has been found that the muon spin precession frequency in fused quartz in an external magnetic field (F _{Q, μ} = 0.116 ± 0.002 MHz) is shifted with respect to that in plastic scintillators (F _{1, μ} = 0.101 ± 0.005 MHz and F _{2, μ} = 0.101 ± 0.002 MHz).     

Influence of impurities on short range electron transport in GaAs

The influence of Cr impurities on muonium atom formation in GaAs has been studied using muon spin relaxation techniques with alternating electric fields. The results suggest that electron transport to and capture by the muon is suppressed by capture/scattering on intervening Cr centers. The length scale involved is estimated to be about 3x10(-6) cm. This offers an opportunity to study electron transport to positive centers in semiconductors on a microscopic scale.     

Dynamics of cyclohexadienyl radicals in NaZSM-5 and LiZSM-5

The dynamics of the muonium substituted cyclohexadienyl radical adsorbed on NaZSM-5 and LiZSM-5 was investigated. Avoided-level-crossing muon spin resonance studies revealed extensive surface-sorbate interactions and showed a strong effect of the nature of the metal dopants on the radical mobility.     

Interaction of anomalous muonium with electronic excitations in Si studied by longitudinal field μSR

We report longitudinal muon spin relaxation measurements in Si doped with phosphorus below room temperature. The data can be described qualitatively in a model where bond-centered muonium is undergoing spin exchange interactions below 150 K. Above this temperature, charge state cycling becomes important.This work is partially supported by the National Sciences and Engineering Research Council of Canada.     

Evidence for muonium emission from an SiO2 layer on n-type Si and the positive muon state in Si

Evidence for the emission of slow muonium atoms from a 3.0-nm-thick SiO₂ layer covered on an n-type Si is reported. Also, upon applying an rf-resonance technique at the muon frequency, a time-differential observation of a delayed state-change from muonium to diamagnetic muon at room temperature was observed. Combining results obtained by use of longitudinal field decoupling and transverse spin rotation methods, the conversion rate was estimated to be 5 to 10 μs⁻¹. Both of the above results, namely the observation of the emission and state-change of muonium, suggest a process in which μ⁺ initially captures an electron from Si, then quickly converts to μ⁺ again during thermal diffusion in the Si towards the SiO₂ layer. Within the oxide layer, muonium is again formed and subsequently is emitted from the SiO₂ surface.     

Low temperature quantum diffusion of muonium in KCl

T ₁ spin relaxation of muonium in KCl has been studied at low temperatures (20 mK to 2 K), where the motion is believed to be band-like, i.e. the mean free path is longer than the lattice constant. The Celio model, based on the assumption of stochastic hopping of muonium, accurately describes the field dependence ofT ₁ at higher temperatures but fails below 4 K. The measuredT ₁ spin relaxation rates vary weakly with temperature below 2 K even thoughk _BT at the lowest temperature is well below the estimated muonium bandwidth obtained from the data at higher temperatures. This is taken as evidence that muonium is not completely thermalized on the time-scale of the muon lifetime due to the weak interaction with phonons at low temperatures.