Quantum diffusion of muons in metals

We consider the influence of electrons on the quantum diffusion of muons in metals. The temperature dependence of the muon-diffusion coefficient is found.     

Quantum diffusion of muons in bismuth

A muon spin relaxation rate in a super-pure sample of bismuth has been measured. The experimental data and the theory of coherent diffusion in crystalline lattices with shifted levels are compared.     

Measuring macroscopic diffusion of positive muons in metals

Conclusions We have discussed some schemes for measuring the diffusion coefficient for positive muons in metals, using diffusion over macroscopic distances. The method offers some promise of yielding diffusion information over wider temperature ranges and a greater variety of metals than the presently used technique. The major difficulty in applying the laminate scheme will be fabricating suitable, well-characterized targets that are thick enough to stop a significant fraction of the ⁺ beam. The use of a surface (i.e., 4 MeV) ⁺ beam appears most promising, but this brings with it formidable technical problems in heating and cooling the targets. We may hope that these problems will be attacked vigorously and effectively in the near future.Research performed under the auspices of the U.S. Department of Energy.     

The localization and thermal diffusion of positive muons in niobium

The depolarization rate for spin polarized ⁺ particles implanted into a high purity niobium crystal was studied as a function of temperature. The results were analyzed in terms of nuclear dipolar field inhomogeneity due to the host⁹³Nb, and the local field averaging effect of the muon's motion. An analysis is presented in terms of the structure of the muon wavefunction and parameters characterizing the muon diffusion.Supported in part by the U. S. National Science FoundationSupported by the U. S. Energy Research and Development AdministrationSupported by the U. S. National Aeronautics and Space Administration     

Quantum diffusion of positive muon in pure tantalum

Quantum diffusion of positive muons has been studied in high purity Ta by zero and longitudinal field muon spin relaxation techniques. We found that the muon hopping rate in Ta is more or less the same as in pure Cu (i.e., \nu\simeq10⁵\sim10⁶\ s^™1), showing a characteristic temperature dependence proportional to T^™\alpha with \alpha ranging from 2 to 0.2 below 20 K. In addition, a step‐like change of the nuclear dipolar width was observed at 60 K associated with the sharp peak of hopping rate, suggesting a change of stable muon sites. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon-spin rotation as a tool for investigating the diffusion of positive muons in type-II superconductors

The measurement of the spin precession frequencies of immobile positive muons in the mixed state of uniformly magnetized type-II superconductors gives the distribution function of the magnetic field. Increasing muon diffusivity leads first to the suppression of the van Hove singularity associated with the field-strength maximum in the flux-line centres, then to an enhancement of the damping of the main precession frequency, and finally to a shift and motional narrowing of the precession frequency distribution. These phenomena can be used to determine muon diffusivities in Nb exceeding about 10^?12m²s^?1. The required information on the magnetic-field distribution function in the mixed state is presented in detail.     

Inhomogeneous quantum diffusion of muons in solids

This article deals with the problems raised when a muon(muonium) quantum diffusion in a crystal is highly inhomogeneous. It is shown how static disorder arising from the crystal doping influence the diffusion process and drastically changes both the time decay of the polarization function and the temperature dependence of the depolarization rate. The spin depolarization of muons moving in a spatially inhomogeneous defect potential and trapping of particles by the long-ranged traps is studied in detail. Most attention is given to the particle localization and delocalization phenomena resulting in the two-component behavior of muon polarization at low temperature. Finally, the experimental data on muon depolarization in insulators KCl, GaAs, N₂ and superconducting metals Al, V are analyzed.     

Antiferromagnetic solid oxygen studied by positive muons

We present a zero magnetic field muon spin rotation study of-O₂ (antiferromagnetic phase of solid oxygen) in the temperature range of 10–24 K. Static magnetic order has been observed below the- transition temperatureB =23.8 K. The temperature dependence of the muon precession frequency exhibits behavior characteristic of a two-dimensional Heisenberg spin-1 system with the anisotropy parameter 10^–2 quite similar to that of antiferromagnetic phase of the high-temperature superconductor parent compounds. A unique local field at the muon site has been determined to beB ₀=1.27(5) kG at low temperatures.     

The use of positive muons in metal physics

The present status of work in metal physics by the new method of “muon spin rotation” is reviewed. This spectroscopy is based on the spin interactions of positive or negative muons and resembles NMR as far as the interpretation of interactions in metals is concerned. The positive muon behaves in several respects as a light isotope of hydrogen in metals. Local properties like site symmetry, local magnetic field, dynamic effects from surrounding spins as well as effects from the diffusion of the particle itself can be measured with high sensitivity.A brief review of the technical aspects is given. The problems of diffusion of light positive particles in metals are discussed, with regard to specific mechanisms at low temperatures, trapping of muons by impurities, etc. The local electronic structure around this kind of impurity in normal metals as well as ferromagnets has been subject to a large nnumber of studies. Other applications include the interaction of muons with other kinds of defects, the study of metal hydrides and measurements on the dynamics of spin glasses.     

Quantum diffusion of the positive muon in the superconducting state of Al

We report low temperature studies of muon diffusion and trapping in Al doped with Li impurities. The trapping rate at Li and the deduced muon diffusion rate increase more rapidly with decreasing temperature in the superconducting state compared with the normal state. The temperature dependence of the quantum diffusion rate in the superconducting state is close to that predicted by the Kondo theory.     

Local fields at positive muons in magnetic substances

The various contributions to the local field at a positive mouon in ferro- and antiferromagnetic substances are discussed. Formulas for the calculation of the dipolar field tensors are derived. The influence of the oscillation of the muon around its equilibrium site is analyzed.Supported in part by the Swiss National Science Foundation.     

Trapping of positive muons by vacancies in non-stoichiometric compounds

A direct evidence for trapping of positive muons by vacancies was found by using the longitudinal field method., 65.5 at. %Cu-34.5 at. %Al, 51at. %Al-49at. %Ni and 52 at. %Al-48at. %Ni polycrystalline samples were studied. The forward/backward asymmetry was measured as a function of time at room temperature changing the magnetic field from 0 to 70 Oe. At H=0, a relaxation function of Kubo-Toyabe type was found. Analysing the data, it was found that positive muons are trapped by vacancies in these materials.     

The anomalous magnetic moment of positive and negative muons

The anomalous g-factor a ≡ (g?2)/2 has been measured for muons of both charges in the Muon Storage Ring at CERN. The two results, a_μ⁺ = 1165910(12) × 10^?9 and a_μ^? = 1165936(12) × 10^?9, are in good agreement with each other, and combine to give a mean a_μ = 1165922(9) × 10^?9, which is very close to the most recent theoretical prediction 1165921(10) × 10^?9. For the experimental results, the total statistical and systematic error is given. The measurements thus confirm the remarkable QED calculation plus hadronic contribution, and serve as a precise verification of the CPT theorem for muons.