Thermal hopping ofμ + between “FμF” centres in NaF

Strongly hydrogen-bonded diamagnetic “FμF” centres are formed by theμ ⁺ in a wide variety of fluoride crystals. Hydrogen atoms are expected to form similar “FHF” complexes. Through the “motional narrowing” of the zero-field muon relaxation function in NaF, we have observed an Arrhenius temperature dependence of the dissociation rate of theFμF complex, yielding a binding energy of 1700 (200) K for theμ ⁺ in theFμF centre.     

Determination of very slow μ+ hop rates in Cu by LLF-μSRhop rates in Cu by LLF-μSR

Muon spin relaxation in low (weak) longitudinal magnetic field (LLF-μSR) provides a means of independently determining the static dipolar width Δ characterizing the μ⁺ lattice site and the correlation time τ_c for μ⁺ hopping, in a manner that is nearly model-independent for τ_c and especially accurate in the near-static limit (τ_c>τ_μ). The advantages of this method are illustrated by its application to muon hopping in Cu near the τ_c maximum around 50 K.     

Galilean and dynamical invariance of entanglement in particle scattering

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.     

The stability of Tenax TA thermal desorption tubes in simulated field conditions on the HAPSITE® ER

Due to the growing need to monitor aircraft cabin, cockpit and breathing-line air quality, functional assessment of sampling equipment for the specialised field conditions of flight need to be established for both in-flight and ground safety. In this article, we assess the reliability of Tenax TA thermal desorption tubes to perform under various relevant field sampling conditions, such as storage temperature, loading temperature, vibrational velocity, gravitational force (G Force) and altitude pressure with semi-real-time gas chromatograph-mass spectrometer (GC-MS) analysis on the field portable HAPSITE^® ER (Hazardous Air Pollutants on Site Extended Range) instrument. First, we show that Tenax TA thermal desorption tubes can handle storage under extreme environmental conditions, 4–77°C, over numerous analytical test cycles. Next, we confirm that extreme loading temperature, both hot (77°C) and cold (4°C), does not affect the analytical reliability of Tenax TA thermal desorption tubes. Then, we illustrate that G Force may have a significant (p ≤ 0.0364) effect on Tenax TA performance while vibrational velocity (p ≤ 0.7265) and low ambient air pressure (p ≤ 0.1753), such as that found at high altitude, do not. Finally, several Tenax TA thermal desorption tubes were flight-tested, demonstrating that the durability of these tubes maybe insufficient for use on military cargo aircraft (p = 0.0107). The results presented here provide a rationale for additional testing of Tenax TA thermal desorption tubes for flight suitability.     

Representations of the Poincaré Semigroup and Relativistic Causality

This paper provides the mathematical tools for addressing issues of two kinds of causality in relativistic scattering theory: general causality, i.e., an effect can only be measured after its cause, and Einstein causality, i.e., no propagation of probability outside of the forward light cone. Starting from Wigner's unitary irreducible representations of the Poincaré group for noninteracting, one particle states, we describe the mathematical tools necessary to describe scattering states, the Lippmann-Schwinger Dirace kets, and to describe resonances and decaying states, the relativistic Gamow ket. An important step for their derivations is the Hardy space hypothesis. Investigating the transformation properties of scattering and resonance states under the dynamical Poincaré semigroup reveals that both kinds of causality result from this hypothesis about nature of the spaces of states and observables.     

μ+knight shifts and trapping in diluteSbSn alloys

Giant μ⁺ Knight shifts K_μ have been studied previously in Sb andSbBi alloys. Here we report μ⁺SR measurements on Sb with dilute heterovalent Sn impurities. A dramatic concentration dependence is observed: K_μ is increased slightly (relative to the value in pure Sb) by Sn concentrations of <0.1%, whereas larger concentrations cause a drastic reduction of K_μ. One concern could be that K_μ values in the alloy might reflect local band structure in trap sites near Sn impurities rather than the bulk “host” band structure of the alloy. This is indeed the case in bothSbSn (0.03%) andSbSn (0.06%), where a second, lower frequency TF-μSR signal begins to appear for T>60K. The amplitude of the low K_μ signal grows with increasing T at the expense of the amplitude of the high-K_μ, low-T signal, suggesting that the μ⁺ migrates through the host lattice to trap sites. A simple trapping model correctly describes the observed T-dependence of the amplitudes, phases and relaxation rates of the two signals. We conclude that the low-T Knight shift is truly characteristic of the host band structure while the much lower K_μ value of the high-T site is characteristic of a specific trap site, presumably adjacent to a Sn impurity.     

Giant muon knight shifts in antimony and antimony alloys

The Knight shift K_μ at the positive muon has been measured as a function of magnetic field, temperature, crystal orientation and alloyed impurity (bismuth or tin) in antimony. The anomalously large and anisotropic K_μ in pure Sb at low temperature has been confirmed and shown to be independent of magnetic field up to 9 kG; its anisotropic part is found to have the same strong temperature dependence as its isotropic component. The addition of 6.3 at.% Bi significantly reduces both K_μ and its anisotropy, but enhances their temperature dependence. The addition of 12.5 at.% Bi, or, more dramatically, as little as 0.3 at.% Sn to antimony is sufficient to reduce K_μ to a small value, effectively eliminating the anomalous behaviour.     

Study of the hybrid state of Y9Co7(2.0≲T≲ 6 K) by means of zero field muon spin relaxation

Muon spin relaxation functions were measured in the magnetic superconductor Y₉Co₇ for T ? 2.0 K and at zero applied field. In the paramagnetic region (T ? 6.0 K) the depolarization of the muon spins is due to the quasi-static ⁵⁹Co nuclear moments. The onset of the magnetic state results in a fast-relaxing signal that corresponds to dipolar fields of the order of 100 0e; this component grows steadily in amplitude as the material transists from the hybrid into the superconducting state. The data are consistent with the high degree of inhomogeneity of the (not long-range) ordering and coexisting but non-competing magnetic and superconducting properties in the “hybrid” state (2<T<5K).     

Hyperfine splitting of muonium in SiO2 powder

The hyperfine splitting of Mu in evacuated SiO₂ powder has been measured over the temperature range 17–300 K using the two frequency method. Above 100 K it is consistent with the vacuum value (4463.3 MHz) indicating the Mu atoms are moving freely between the particle grains. At lower temperatures it drops rapidly to 4437±4 MHz at 17 K. The effect is attributed to thermal adsorption on the SiO₂ surface. Measurements were also made on an Ar coated powder between 7–62 K. The hyperfine splitting is consistent with the vacuum value over this range.