Quantum diffusion of muonium in GaAs

The diffusion rate of muonium in the III–V compound semiconductor GaAs has been determined from measurements of muon spinT ₁ relaxation induced by motion in the presence of nuclear hyperfine interactions. It is shown for the first time in a semiconductor that (a) there is a crossover of the transport mechanism at about 90 K from stochastic to zero-phonon hopping, as evidenced by a steep rise in the hop rate at lower temperatures, and that (b) the muonium diffuses at the hop rate of 10¹⁰ s⁻¹ (corresponding diffusion constantD≈10⁻⁶ cm²s⁻¹) at lower temperatures as well as at room temperature.     

Muon/Muonium in an Isotopically Pure 13C Diamond

A preliminary study of the diamagnetic (μ_d) and the paramagnetic (Mu _T ) states in a synthetic ¹³C diamond has been performed using the Transverse Field Muon Spin Rotation method. This system could be used to verify the quantum diffusion behaviour observed before, however, with a more reliable extraction of the hopping rate. The results were obtained in an applied magnetic field of 7.5 mT and at sample temperatures of 10 K, 100 K and 200 K. The prompt fraction, f, of the μ_d state remains constant at 22(5)% in the range 10–200 K; that of the Mu _T state increases from 53(10)% at 10 K to 78(10)% at 200 K. The fractions of the two states add to 100% at 200 K, suggesting non-population of the bond-centred state, Mu_BC, which is often observed in other diamond samples. The μ_d state has a spin relaxation rate of 0.20(5) μs⁻¹, in contrast to the zero value obtained in type II diamond samples. This indicates appreciable interaction of the μ_d state with the ¹³C atoms. The Mu _T state has a large spin relaxation rate ranging from 3.0(5) μs⁻¹ at 10 K to 7.0(5) μs⁻¹ at 200 K, consistent with values obtained in diamond samples with defects. This work is part of ongoing studies of muon/muonium-defect interactions in diamonds. This revised version was published online in September 2006 with corrections to the Cover Date.     

Experimental investigation of muon-catalyzed t + t fusion

The muon-catalyzed fusion (μCF) process in tritium was studied by the μCF collaboration on the muon beam of the JINR Phasotron. The measurements were carried out with a liquid tritium target at the temperature 22 K and density approximately 1.25 of the liquid hydrogen density (LHD). Parameters of the μCF cycle were determined: the ttμ muonic molecule formation rate λ _ttμ = 2.84(0.32) μs⁻¹, the ttμ fusion reaction rate λ _f = 15.6(2.0) μs⁻¹, and the probability of muon sticking to helium ω _tt = 13.9(1.5)%. The results agree with those obtained earlier by other groups, but better accuracy was achieved due to our unique experimental method. The article is published in the original.     

A μSR and neutron polarisation analysis study of Mn moment delocalisation in Fe substituted YMn2

Neutron polarisation analysis measurements reveal antiferromagnetic spin correlations persisting to temperatures of 120 K in Pauli paramagnetic Y(Mn_1−x Fe _x )₂, 0.03≤x≤0.05. The mean moment at the Mn(Fe) site is found to be 0.2μ _B. Transverse field μSR is characterised by weak exponential damping with a rate of 0.02 μs⁻¹ at 300 K increasing according to the power lawT ^−0.75 to only 0.16μ _S ⁻¹ at 12 K. It is suggested that these results are consistent with a slowing down of longitudinal spin fluctuations at the Mn site as temperature decreases.     

The μSR study of the relaxation of Ho and Er magnetic moments in high-Tc 1-2-3 compounds

High temperature superconductors HoBa₂Cu₃O_7−δ (T _c ≅93 K), Ho_0.5Y_0.5Ba₂Cu₃O_7−δ (T _c ≅93 K) and ErBa₂Cu₃O_7−δ (T _c ≅95 K) were investigated by the zero-field μSR-technique. The muon spin depolarisation rate connected with the fluctuation frequency of rare-earth ion magnetic moments was measured. It was found that the samples with holmium show a fast increase of the muon spin depolarisation rate at temperatures below 20 K, while in ErBa₂Cu₃O_7−δ the depolarisation rate remains low in the whole temperature region studied (4.2 K-270 K). The sharp difference between the behaviours of the muon spin depolarisation rate may be explained by the difference between the ground state of Ho³⁺ and Er³⁺ ions in the crystalline field of the lattice.     

Stability of muon-oxygen bond sites in RBa2Cu3O7

Relative energies of muon probe sites in the chain region of RBa₂Cu₃O₇ (RBCO) are investigated using a molecular quantum chemistry calculation for (Oμ)⁻ embedded in a cluster of point charges to simulate local charge distributions in RBCO. Partial Cu−O chain covalency results in a O-μ...O muon site between the chain and bridging oxygens. However, Cu-μ “hydride”-like sites are suggested by results for nominally ionic clusters.     

Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

Longitudinal field relaxation measurements in monocrystalline DyAl2

Longitudinal μSR measurements were performed on a single crystal sphere of DyAl₂ in the range 4K≤T≤300 K (i.e. both in the ferromagnetic and paramagnetic phases). Contrary to previous reports the dynamic depolarization rate does not diverge near T_C≌65 K. Rather a well defined peak in the depolariation rate is observed around 95 K with 1/T₁ (95 K)∼4 μsec⁻¹. The depolariztion rate above T_C is field independent in the range 0≤B_ext≤2.5 kG. The observed behavior may be accounted for by assuming that the effective correlation time τ is given by τ⁻=τ _4f ⁻¹ +τ _diffusion ⁻¹ . The field independence requires that τ_eff<2·10⁻¹¹. The peak in 1/T₁ could then reflect a slowing down in μ⁺.     

Muon diffusion in Nb−H systems

We have studied the muon diffusion in various Nb−H_X systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ⁺ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.     

Muons in type-II superconductors: μ+ diffusion in ultra-pure niobiumdiffusion in ultra-pure niobium

The diffusivityD _μ of positive muons (μ⁺) in the mixed state of superconducting high-purity, high-perfection niobium single crystals is investigated by measurements of the relaxation of the transverse muon spin polarization (μ⁺SR). The method makes use of the strong magnetic field gradients existing in the mixed state of Type-II superconductors and monitorsD _μ through the variation of the magnetic field felt by the μ⁺ during their diffusion through the crystals. For μ⁺ near the centres of the flux lines inNb it givesD _μ(4.6 K)=(8±2)·10⁻¹¹m²S⁻¹. The positive temperature coefficient ofD _μ indicates that at liquid-helium temperatures the diffusivity of μ⁺ inNb is mainly due to phonon-assisted tunnelling processes.     

Negative muon spin precession in ferromagnetic iron and the hyperfine anomaly

The hyperfine field (B _μ ^hf ) at the negative muon μ⁻ in ferromagnetic iron was investigated by means of the zero-field μ⁻ spin precession technique. In the temperature range 320–690 K,B _μ ^hf for μ⁻ Fe departs from the magnetization curve of pure iron in the same way as the hyperfine field seen by a⁵⁵Mn impurity in dilute MnFe measured by NMR. The hyperfine anomaly for μ⁻ Fe relative to dilute (1.5 at.%)⁵⁵Mn in iron is found to be −0.9(3)% and temperature independent over the temperature range investigated.     

Dielectric spectroscopy of PbZr1 ? xTixO3 solid solutions (0.495 ≤ x ≤ 0.51) in a temperature range of 100–300 K at frequencies from 1 × 10?2 to 2 × 107 Hz

The behavior of the relative permittivity ɛ/ɛ₀ of PbZr_{1 − x} Ti _x O₃ (PZT) solid solutions (0.495 ≤ x ≤ 0.51) in the temperature range of 100–300 K at frequencies from 1 × 10⁻² to 2 × 10⁷ Hz was investigated. Diffuse, strongly relaxing maxima at T = 230−260 K (x = 0.495−0.505) and 150–160 K (x = 0.510) were observed in the PZT studied. The relaxation processes are well described by the Vogel-Fulcher law, and the dielectric spectra are approximated by the Cole-Cole formula.     

Investigation of low-temperature quantum diffusion in α-iron byμ + SR experiments on a single-crystal sphereSR experiments on a single-crystal sphere

The longitudinalμ ⁺-spin relaxation rate has been measured on a high-purity spherical α-iron single crystal at temperaturesT down to 20 mK and in applied magnetic fieldsB _appl parallel to 〈111〉 up to 3 T. Only above 1 K can the data be satisfactorily described by one rate constantГ. At 1 T≤B _appl≤2 T and 50 mK≤T≤300 mK, oscillations (“wiggles”) were in addition superimposed on the longitudinal relaxation. A qualitative understanding of the measurements may be achieved in terms of the increasing influence of internal stresses onμ ⁺ diffusion as the temperature is lowered.     

Investigation of the Parameters of Muon-Catalyzed Fusion in Double D/T Mixture at High Temperature and Density

Experiments on the study of the muon catalyzed fusion (μCF) process in a double D/T mixture of hydrogen isotopes in the temperature range 300–800 K at densities 0.3–0.5 LHD are performed at the JINR phasotron. The values of the effective μCF parameters (cycling rate λ _c , neutron yield Y _n , muon losses w) are obtained. Tentative dtμ-molecule formation rates on D₂ and DT molecules (λ _dtμ−d and λ _dtμ−t ) are obtained for different mixture temperatures and densities. The results obtained show that λ _dtμ−t increases with temperature, but its value is smaller than theoretical predictions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Zero-field muon spin rotation in monocrystalline chromium

Spin precession of positive muons in chromium in zero applied magnetic field is reported for the first time. The observations cover the temperature range from about 2.5 K to 10 K and thus pertain to the so-called longitudinal spin-density wave (LSDW) state of antiferromagnetic Cr. The conclusions that may be drawn from the existence of one rather sharp spin precession line are discussed, among them the estimateD _μ=2.4·10⁻¹⁴ m² s⁻¹ for the muon diffusivity at 4 K. Considerable evidence exists for a strong interactions of μ⁺ with the charge-density waves that are likely to accompany the LSDWs in Cr.     

The Muonic Hydrogen Lamb Shift Experiment at PSI

A measurement of the 2S Lamb shift in muonic hydrogen (μ⁻p) is being prepared at the Paul Scherrer Institute (PSI). The goal of the experiment is to measure the energy difference ΔE(2⁵ P _3/2−2³ S _1/2) by laser spectroscopy (λ≈6μm) to a precision of 30 ppm and to deduce the root mean square (rms) proton charge radius with 10⁻³ relative accuracy, 20 times more precise than presently known. An important prerequisite to this experiment is the availability of long-lived μp_2S -atoms. A 2S-lifetime of ∼1 μs – sufficiently long to perform the laser experiment – at H₂ gas pressures of 1–2 hPa was deduced from recent measurements of the collisional 2S-quenching rate. A new low-energy negative muon beam yields an order of magnitude more muon stops in a small low-density gas volume than a conventional cloud muon beam. A stack of ultra-thin carbon foils is the key element of a fast detector for keV-muons. The development of a 2 keV X-ray detector and a 3-stage laser system providing 0.5 mJ laser pulses at 6 μm is on the way. This revised version was published online in August 2006 with corrections to the Cover Date.     

Frequency shift and relaxation of muon-spin-precession in Cd1−xMnxTe

Transverse-field muon spin roation (μSR) is studied in Cd_1−xMn_xTe, x=0.4 and 0.6 mixed crystals. A large temperature dependent frequency shift and a strong relaxation of the μSR-signal are observed. In the vicinity of the spinglass transition, the relaxation rate becomes so large that the signal disappears. The rate of Mn spin fluctuations causing the μ⁺-line narrowing at high temperatures is estimated to be of the order of 10⁹ S⁻¹.     

Properties of Hg implanted Hg1? x Cd x Te infrared detectors

Experimental performance parameters of Hg implanted Hg_1−x Cd _x Te photovoltaic detectors are analyzed. At 77K, for 8–14 μm band, a comparison is made between performances and theoretical ultimate diffusion limits in low frequency direct detection. Experimental features are well-explained by a model based on the Auger band-to-band process for carrier recombination. Peak detectivities exceeding 10¹¹ cm Hz^1/2W⁻¹, external quantum efficiencies as high as 90%, and zero-bias resistance-area products better than 1 Ω·cm² have been achieved in devices with 12 μm cutoff wavelengths. In the 3–5 μm band performances are far from the diffusion limit. Notwithstanding, at 77K zero-bias resistance-area products are better than 10⁴Ω·cm² and detectivities of the order of 10¹² cm Hz^1/2W⁻¹ were observed at 5 μm. Predominant generation-recombination contribution are present at room temperature in 1–1.3 μm photodiodes whose detectivities, primarily limited by the Johnson noise, at 1.3 μm are higher than 10¹¹ cm Hz^1/2W⁻¹ at 300 K. The high frequency response of the photodiodes is also discussed. Response times as low as 0.5 ns are reached despite some limitations arising from the implanted layer sheet resistance. Work supported by CNR-CISE contract No. 73.01435.     

Comparative Theoretical Study of Hyperfine Interactions of Muonium in A- and B-Form DNA

Muon Spin Relaxation (μSR) experiments in A- and B-form DNA have shown evidence for an enhanced electron mobility in the more closely-packed A-form. Besides dynamic effects (electronic diffusion) that could cause the observed difference in muon spin relaxation, one should also carefully examine the difference in the strengths of the hyperfine interactions of the muon (μ ⁺) with the moving electron in the two forms of DNA, since this could contribute to the observed difference in the muon spin relaxation rates as well. We have therefore investigated the (static) trapping properties of muon and muonium (μ ⁺ e ⁻) in A-form and B-form DNA from first-principles with the aim to understand how the different structural geometries of A- and B-form DNA can influence the hyperfine interaction of trapped muonium.     

Total and transport elastic cross-sections for excited muonic and pionic hydrogen atoms

The results of an experiment on muon catalyzed dd-fussion in HD gas are presented. The experiment was performed at the muon beam of PSI using a high-pressure ionization chamber filled with pure HD-gas of low D₂ concentration on the level 1%, at temperatures 50, 150 and 300 K. The non-resonant character of ddμ-molecule formation on HD molecules was confirmed by measuring the ratio of yields of the two ddμ-fusion channels, R=Y(³He,n)/Y(³H,p), which proved to be close to unity. The ddμ formation rate was found to vary from λ_ddμ-HD=0.05· 10⁶ s^-1 at T=50 K to λ_ddμ-HD=0.12· 10⁶ s^-1 at T=300 K, in agreement with the theoretical prediction. A prominent peak at t<60 ns was observed in the time spectrum of fusion neutrons indicating a resonant contribution of ddμ formation from epithermal dμ atoms. This revised version was published online in August 2006 with corrections to the Cover Date.