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.     

Physical applications of muon catalysis: Muon capture in hydrogen

Results of theoretical and experimental research on capture of negative muons in hydrogen are reported with an emphasis on the accompanying phenomenon of muon catalysis in hydrogen and subtleties of the experimental method. A conclusion is drawn that precise determination of the capture rate is important for refining the standard model.     

Experiments with low-energy muons

Two experiments with low-energy muons are described: the determination of the stopping power of C, Si, Ti and Au for muons at energies down to 2 keV and the measurement of the diffusion times for pµ and dµ atoms in low-pressure (0.25–12 hPa) hydrogen gas. A pronounced Barkas effect was found for muons at the Bragg peak (about 10 keV): the stopping power for µ^– in C, e.g., is about 30% lower than that for µ⁺. The mean kinetic energy of pµ atoms at the end of the cascade in 1 hPa hydrogen gas was determined to be (2.6 ± 0.6) eV (preliminary value).     

Study of the charge asymmetry in electromagnetic interactions of cosmic ray muons

The Durgapur cosmic ray spectrograph has been utilised to study the electromagnetic interaction of cosmic ray muons in iron in the momentum range 5–100 GeV/c. The dependence of the interaction cross section on the charge of the muons for the production of a single electron secondary due to the knock-on process and for two and more two electrons due to both knock-on and pair production has been investigated.The ratio of the interaction cross section for positive muons to that for negative muons in the magnetic-iron has been found to be 0.952 ± 0.045 for the production of one secondary particle. For production of two and more than two secondaries the ratios are 1.05 ± 0.09 and 0.91 ± 0.08 respectively. The present results do not indicate any charge asymmetry of cosmic ray muons in respect of electromagnetic interactions in iron.     

On the theory of diffusion of light interstitials in metals

Using a nonlinear-screening approach the potential energy of positively charged light interstitials in Cu and lattice distortions around these particles have been determined numerically. The calculations predict a marked isotope effect for the lattice distortions around positive muons and protons at octahedral interstitial sites. They indicate that in Cu the diffusion mechanisms for positive muons and for hydrogen isotopes may be different.     

Separation of positive and negative muons in a giant shower by the geomagnetic field

The separation of positive and negative muons in a giant shower by the geomagnetic field is observed at a very high level of significance 0.03%. This result is obtained by interpreting in terms of the quark-gluon string model the indications of all detector stations that were triggered in this shower (which was detected at the Yakutsk array) on the basis of calculations of the responses of these stations both with and without taking the Earth’s magnetic field into account. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 177–182 (10 August 1998)     

The Coulomb capture of negative muons by hydrogen atoms in the non-adiabatic close-coupling approximation

We present some results obtained within the non-adiabatic close-coupling approximation for Coulomb capture during collisions of slow negative muons with hydrogen atoms. The calculations are performed in momentum-space and a statistical distribution analysis is used to obtain the final cross sections. The present model results are in harmony with existing calculations. We conclude that further calculations within the present approach are justified.     

Dynamics of muonic atom cascade in hydrogen-helium mixtures

The deexcitation of excited muonic protium and deuterium in the mixture of hydrogen and helium isotopes is considered. Methods of experimental determination of the probability of direct atomic muon capture by hydrogen and muon transfer rates from excited muonic hydrogen to helium are proposed. Theoretical results for the population of the muonic atoms in the ground state, , are compared with the existing experimental data. Results obtained for mixtures are of interest for investigation of nuclear fusion in muonic molecules. Received: 6 August 1998 / Revised: 1st October 1998 / Accepted: 2 October 1998     

The depolarization of muons in solid hydrogen

The relaxation rate (ξ) of the spin of positive muons has been measured in hydrogen containing 2%; 55% and 66% O−H₂ in the temperature range 1.5 to 20 K in a transverse magnetic field of 286 gauss.     

Time-evolution of cascade processes of muonic atoms in hydrogen-helium mixtures

The time-dependence of the population of muonic hydrogen states in hydrogen-helium mixtures is calculated for principal quantum number n. The number of muons transferred to helium nuclei is also determined. The dependence of the population of the ground state of muonic hydrogen on time and target density and the helium concentration is also considered. The results are in agreement with recent experimental data. The comparison of the calculated yield of K lines of X-ray in pure hydrogen and deuterium with experimental data indicates the essential role of the Coulomb deexcitation process. Possible Stark mixing is also analysed. Received 17 February 1999 and Received in final form 9 June 1999     

Shear modulus and compliance in the range of the dynamic glass transition for metallic glasses

High-resolution synchrotron-radiation powder diffraction experiments were performed to observe structural changes induced by hydrogen loading in rapidly-quenched Ti-Zr-Ni alloy ribbons with dominant icosahedral character. Lattice expansion effects due to hydrogen storage in Ti-Zr-Ni quasicrystals as well as phonon and phason disorder coefficients are obtained from an analysis of diffraction linewidths. Received: 26 August 1997 / Revised: 8 January 1998 / Accepted: 10 February 1998     

Antiproton-hydrogen scattering at low-eV energies

In the scattering of negative particles other than the electron by atoms at lab-frame energies around 10 eV, an elastic process termed “brickwall scattering” might lead to a high probability for scattering angles around 180°. For an antiproton slowing in hydrogen, this backward scattering would result in the loss of nearly all of its energy in a single collision, since it and a hydrogen atom have nearly the same mass. Such energy loss would have a significant effect on the energy distribution of antiprotons at energies where capture by the protons of hydrogen is possible and might, thereby, affect the capture rate and the distribution of capture states. In the semiclassical treatment of the problem with an adiabatic potential energy, brickwall scattering is indeed present, and with a substantial cross section. However, this model appears to underestimate inelastic processes. Based on calculations for negative muons on hydrogen atoms, these processes appear to occur for about the same impact parameters as brickwall scattering and thus substantially reduce its effect.     

The investigation of defects in metals with positive muons

It is shown that the trapping of positive muons by defects in metals attracting positively charged particles may be used to investigate such defects in considerable detail by spin relaxation of positive muons.     

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.     

Level crossing resonance detection of a muonic radical in sulphur

Detection of a level crossing resonance establishes that a molecular radical is created in elemental sulphur following the implantation of positive muons. Formally this is the product of the reaction of atomic muonium with the S₈ rings and must serve as a model for the fate of interstitial atomic hydrogen in this element. The isotropic component of the muon-electron hyperfine interaction is determined to be 233 ± 5 MHz. Preliminary data for the temperature dependence of the resonance linewidth indicates a substantial motional narrowing of the anisotropic components.     

Radical reorientation dynamics studied by positive-muon avoided level crossing resonance

Spin polarised positive muons substituted for a hydrogen nucleus in organic radicals are used as spin labels to sense reorientational motion of the radicals in orienting environments. The effect of uniaxial motion on the spectrum of the muonated cyclohexadienyl radical in a benzene single crystal and of its hexamethyl derivative in polycrystalline hexamethylbenzene is demonstrated. Isotopic spectra for cyclohexadienyl radicals adsorbed on SiO₂ are explained by translational diffusion around the 7 nm grain. The potential of the technique to study transient radical intermediates of processes in heterogeneous catalysis is discussed.     

Frictional accumulation of negative muons and its application

A novel method is proposed for the efficient conversion of intermediate energy negative muons into a low-energy muon beam. It is based on using an electric field to eject muons from a moderator consisting of a large number of thin carbon foils placed perpendicularly to the axis of a high-field solenoid. High-energy muons are made to slow down within the moderator to an energy where further slowing down is inhibited by the electric field acceleration between the foils. The muons accumulate at low energy within the moderator hopping from one foil to the next until they come out as a low-energy muon beam. The resulting phase compression factor exceeds 1000. Efficient initial injection of the muons into the moderator is obtained either by letting the muons enter it in a direction opposite to the acceleration force or by producing the muons within a magnetic trap containing the moderator. A practical configuration based on the second scheme is presented. By implementing the method into the most intense muon production configurations a new pathway is opened that may ultimately compete with other schemes in the selection of the optimal source for high-energy muon colliders.     

Detection of hydrogen isotope atoms by mass spectrometry combined with resonant ionization

We examined the application of mass spectrometric methods using resonant ionization by a tunable laser and proposed its use for analyzing hydrogen isotopes. We conducted resonance ionization mass spectrometry (RIMS) to detect gas-phase hydrogen isotope atoms. The ionization efficiency was increased by more than 1000 times that obtained with conventional methods using nonresonant ionization. Resonant laser ablation mass spectrometry (RLAMS) was applied for deuterium detection in solid samples. A graphite substrate implanted with deuterium was used for ordinary laser ablation mass spectrometry (LAMS) and RLAMS. The deuterium signal was observed very clearly by RLAMS, in contrast to LAMS. Mass spectrometry combined with resonance ionization was very useful for hydrogen isotope detection, because components with equal mass numbers were resolved and the method demonstrated higher ionization efficiency. Received: 4 November 1998 / Revised version: 12 January 1999 / Published online: 7 April 1999     

Sites and diffusion for muons and hydrogen in titanium hydrides

Low temperature sites for muons implanted in TiHx have been found to be a mixture of interstitial and substitutional sites, with substitutional occupancy determined by the probability that a muon in an interstitial site will have a vacant nearest neighbor substitutional site. As with ZrHx, activation from the interstitial site is observed below 300 K. From the depolarization rate in the substitutional site, the muon likely displaces the neighboring H atoms by about 0.1 A. Diffusion for the substitutional muons occurs above room temperature with an activation of about 0.38 eV, which is less than the 0.505 eV for hydrogen vacancy motion observed by NMR. To explain this the muon transition rate to a vacancy must be less than that of hydrogen.     

Investigation of acceptor centers in semiconductors with the diamond crystal structure by the μ − SR method

The residual polarization of negative muons in crystal silicon samples with phosphorus (P: 1.6×10¹³ cm⁻³) and antimony (Sb: 2×10¹⁸ cm⁻³) impurities is investigated. The measurements are made in a 1000 G magnetic field oriented in a direction transverse to the muon spin in the temperature range 4–300 K. The relaxation rate and shift of the precession frequency in the silicon sample with the phosphorus impurity are measured more accurately than previously. It is found that in antimony-doped silicon the acceptor center _μ A1 at temperatures below 30 K can be in both ionized and neutral states. The experimental data are interpreted on the basis of spin-lattice relaxation of the magnetic moment of an acceptor center, formation of acceptor-donor pairs, and recombination of charge carriers at the acceptor. Preliminary measurements showed a nonzero residual polarization of negative muons in germanium. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 61–66 (10 July 1998)