Search

This paper reports measurements of the temperature dependence of the rate constants for H-atom abstraction reactions from propane and n-butane by the light isotopic H-atom muonium (Mu), kMu(T), over temperatures in the range 300 K to 435 K. Simple Arrhenius fits to these data yield activation energies, EMua, that are some 2–4 times lower than EHa found from corresponding fits for the H + propane and H + n-butane reactions studied elsewhere, both experimentally and theoretically, and fit over a similar temperature range. These activation energies EMua are also much lower than estimated from zero-point-energy corrected vibrationally adiabatic potential barriers, both results suggesting that quantum tunneling plays an important role in determining kMu(T) and for the Mu + propane reaction in particular. The results are expected to pose a considerable challenge to reaction rate theory for isotopic H-atom reactions in alkane systems.

Calculations of kinetic isotope effects (KIEs) provide challenging tests of quantal mass effects on reaction rates, and muonium KIEs are the most challenging. Here, we show that it can be very important to include reaction-coordinate-dependent vibrational anharmonicity along the whole reaction path to calculate tunneling probabilities and KIEs. For the reaction of propane with Mu, this decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants. Our results agree well with the experimental observations.

Precise measurements of the muonium (Mu) hyperfine interaction versus temperature are reported in a silica aerogel and mesoporous silica SBA-15 using a fast-timing spectrometer to detect the precession frequencies of Mu in a magnetic field of 1.14 T. The observed signals are a sensitive monitor of dynamics associated with the binding and unbinding of Mu from the silica surface. Above 100 K the Mu is effectively off the surface. Significant differences are observed in the way the lines show motional narrowing, and are attributed to differences in sample morphology. At room temperature the effective mean free path appears longer in SBA-15, suggesting it may offer advantages over aerogel as a source of Mu in vacuum.

We report the reaction of muonium (Mu = [μ+e-]), a light isotopic analog of hydrogen, with uncapped gold nanoparticles embedded in mesoporous silica. Using the radio-frequency muon spin rotation (RF-μSR) technique, we directly observe and characterize the resulting final state on the nanoparticle surface, showing conclusively its diamagnetic nature. The magnetic environment experienced by the reacted muons is only weakly perturbed compared to that of muons in a silica reference, consistent with the surface of the gold nanoparticles being metallic and non-magnetic. We demonstrate the potential of RF-μSR for the investigation of the surface properties of nanoparticles and show the feasibility of Knight shift measurements of muons on metal surfaces.

Gold nanoparticles (AuNPs) have been a subject of considerable interest in recent years due to both their magnetic and catalytic properties. This paper reports a two-fold study of the reactivity at...

Isotopic substitution of muonium for hydrogen provides an unparalleled opportunity to deepen our understanding of quantum mass effects on chemical reactions. A recent topical review in this journal of the thermal and vibrationally state-selected reaction of Mu with H2 raises a number of issues that are addressed here. We show that some earlier quantum mechanical calculations of the Mu + H2 reaction, which are highlighted in this review, and which have been used to benchmark approximate methods, are in error by as much as 19% in the low-temperature limit. We demonstrate that an approximate treatment of the Born–Oppenheimer diagonal correction that was used in some recent studies is not valid for treating the vibrationally state-selected reaction. We also discuss why vibrationally adiabatic potentials that neglect bend zero-point energy are not a useful analytical tool for understanding reaction rates, and why vibrationally non-adiabatic transitions cannot be understood by considering tunnelling through vib...

We report a new advance in the study of muonium (Mu) reactivity; specifically, we report the rate constant for the Mu + H2(vibrational quantum number n = 1) reaction determined by measurements at 300 K and by converged quantum mechanical calculations. Comparisons are made with earlier results for D + H2 (n = 1) and with the corresponding thermal reaction rates. The measurements are a sensitive probe of the high-curvature region in the entrance valley of the potential energy surface (PES) and thus provide a qualitatively different probe of the PES than that provided by any previous experiment.

The hyperfine coupling constants (HFCCs) of all the butyl radicals that can be produced by muonium (Mu) addition to butene isomers (1- and 2-butene and isobutene) have been calculated, to compare with the experimental results for the muon and proton HFFCs for these radicals reported in paper II (Fleming, D. G.; et al. J. Phys. Chem. A 2011, 10.1021/jp109676b) that follows. The equilibrium geometries and HFCCs of these muoniated butyl radicals as well as their unsubstituted isotopomers were treated at both the spin-unrestricted MP2/EPR-III and B3LYP/EPR-III levels of theory. Comparisons with calculations carried out for the EPR-II basis set have also been made. All calculations were carried out in vacuo at 0 K only. A C-Mu bond elongation scheme that lengthens the equilibrium C-H bond by a factor of 1.076, on the basis of recent quantum calculations of the muon HFCCs of the ethyl radical, has been exploited to determine the vibrationally corrected muon HFCCs. The sensitivity of the results to small variations around this scale factor was also investigated. The computational methodology employed was "benchmarked" in comparisons with the ethyl radical, both with higher level calculations and with experiment. For the β-HFCCs of interest, compared to B3LYP, the MP2 calculations agree better with higher level theories and with experiment in the case of the eclipsed C-Mu bond and are generally deemed to be more reliable in predicting the equilibrium conformations and muon HFCCs near 0 K, in the absence of environmental effects. In some cases though, the experimental results in paper II demonstrate that environmental effects enhance the muon HFCC in the solid phase, where much better agreement with the experimental muon HFCCs near 0 K is found from B3LYP than from MP2. This seemingly better level of agreement is probably fortuitous, due to error cancellations in the DFT calculations, which appear to mimic these environmental effects. For the staggered proton HFCCs of the butyl radicals exhibiting no environmental effect in paper II, the best agreement with experiment is consistently found from the B3LYP calculations, in agreement also with benchmark calculations carried out for the ethyl radical.

Stimulated Raman pumping (SRP) is used to produce H 2 in its first vibrational state, in order to measure, for the first time, the Mu + H 2 * ( v = 1 ) → MuH + H reaction rate at room temperature, as a prototypical example of new directions in gas-phase muonium chemistry, utilizing the pulsed muon beam and a new dedicated laser system at the RIKEN/RAL Laboratory. Reported here is a preliminary result but the final results are expected to provide definitive new tests of reaction rate theory on the highly accurate H 3 potential energy surface. The major difficulty in this experiment, compared to the standard SRP process, is to ensure a homogeneous excitation over a volume of several cm 3 and of sufficient intensity to ensure a measurable Mu relaxation rate. The techniques used to accomplish this are described. The experiment utilizes the 2nd harmonic output of a Nd:YAG laser (532 nm) with pulse energies up to 500 mJ at a repetition rate of 25 Hz. Different optical setups have been constructed and tested in order to optimize the number of laser-pumped H 2 molecules and their overlap with the stopping profile of the muon beam in the reaction cell (total volume ∼ 100 × 40 × 4 mm 3 ). The first result of this experiment gives a measured relaxation rate due to laser excitation of λ * = 0.085 ± 0.051 μ s - 1 , consistent with theory but limited by both low statistics and particularly a high background relaxation rate.

The kinetics of the addition reaction of muonium (Mu) to acetylene have been studied in the gas phase at N2 moderator pressures mainly from ∼800 to 1000 Torr and over the temperature range from 168 to 446 K, but also down to 200 Torr at 168 K and over a much higher range of pressures, from 10 to 44 bar at 295 K, demonstrating pressure-independent rate constants, kMu(T). Even at 200 Torr moderator pressure, the kinetics for Mu + C2H2 addition behave as if effectively in the high-pressure limit, giving k∞ = kMu due to depolarization of the muon spin in the MuC2H2 radical formed in the addition step. The rate constants kMu(T) exhibit modest Arrhenius curvature over the range of measured temperatures. Comparisons with data and with calculations for the corresponding H(D) + C2H2 addition reactions reveal a much faster rate for the Mu reaction at the lowest temperatures, by 2 orders of magnitude, in accord with the propensity of Mu to undergo quantum tunneling. Moreover, isotopic atom exchange, which contributes in a major way to the analogous D atom reaction, forming C2HD + H, is expected to be unimportant in the case of Mu addition, a consequence of the much higher zero-point energy and hence weaker C-Mu bond that would form, meaning that the present report of the Mu + C2H2 reaction is effectively the only experimental study of kinetic isotope effects in the high-pressure limit for H-atom addition to acetylene.

In this paper, we report preliminary data for the first direct evidence of a free radical formed from Mu reactivity with Br 2 in the gas phase, in N 2 moderator at a total pressure of 3 bar. A new experimental setup and target vessel for μSR studies of reactive compounds, such as the halogens and hydrogen halides, suitable as well for RF measurements, is described. The experimental data, obtained from a longitudinal field repolarization curve, yields a hfc of 1770 MHz. We tentatively identify this as the [BrMuBr] radical, a non-conventional bond system, arising from the combination of a van der Waals interaction and dynamics on a repulsive surface. Studies of the dynamics and hfcs of possible radicals, which in principal could form, are also outlined here.

Diamagnetic and muonium (Mu) fractions formed in low-pressure inert gases, by energetic muon implantation, have been studied using the technique of time-delayed radio frequency muon spin resonance (RF-μSR). Results obtained establish the validity of the long-held view that formation of these species is due only to prompt processes, and in turn confirms that the diamagnetic environment is due to a muon molecular ion, MMu+, and not a bare μ+. In addition, polarization fractions for the diamagnetic and Mu environments have been determined at different pressures, thereby complementing earlier data, and demonstrating that the RF-μSR technique provides polarization fractions in good accord with those obtained using conventional transverse-field muon spin resonance measurements.

Muonium has been directly detected over a range of temperatures and fields by transverse field μSR in different zeolites: 3A, 13X, USY, ZSM-5, and S-115 (a high-silica form of ZSM-5), as well as in silica gel. The polarizations determined from data at 75 and 150 G were independent of both field and temperature. The amounts of Mu seen vary from ∼20% to 40%, with a large missing fraction seen in every case, which may be partly due to slow Mu formation. There is also a fast Mu relaxation rate seen in all samples. This is the first direct observation of Mu in zeolites.

The adsorption and dynamical behavior of the muonated cyclohexadienyl radical (C6H6Mu) in NaY zeolite, formed by muonium (Mu) addition on adsorbed benzene, was investigated by the muon spin resonance (μSR) technique, primarily at loadings of 2−3 C6H6 molecules per supercage of NaY. The dynamics of this radical are expected to be the same as its isotopic analogue, C6H7, for which there are no similar data available. Both TF-μSR and ALC-μSR spectra were recorded, with the most detailed information provided by the positions and line widths of the avoided level crossing resonances. In concert with 2H NMR, neutron diffraction and molecular dynamics studies of the parent benzene molecule, as well as current theoretical calculations, the dominant adsorption site for the C6H6Mu radical is believed to be the SII Na cation, within a supercage, which gives rise to three observed ALC lines, corresponding to two different orientations for the muon (proton) of the CHMu methylene group: pointing toward (endo) and away ...

Isotope effects are important in the making and breaking of chemical bonds in chemical reactivity. Here we report on a new discovery, that isotopic substitution can fundamentally alter the nature of chemical bonding. This is established by systematic, rigorous quantum chemistry calculations of the isotopomers BrLBr, where L is an isotope of hydrogen. All the heavier isotopomers of BrHBr, BrDBr, BrTBr, and Br(4)HBr, the latter indicating the muonic He atom, the heaviest isotope of H, can only be stabilized as van der Waals bound states. In contrast, the lightest isotopomer, BrMuBr, with Mu the muonium atom, alone exhibits vibrational bonding, in accord with its possible observation in a recent experiment on the Mu+Br2 reaction. Accordingly, BrMuBr is stabilized at the saddle point of the potential energy surface due to a net decrease in vibrational zero point energy that overcompensates the increase in potential energy.

The hyperfine coupling constant A of a hydrogen isotope confined in a cage differs from its vacuum value, demonstrating that the atom acts as a probe of its environment. Room-temperature values of A for muonium in different cube-shaped Si8O12 units (T8 units or octasilsesquioxanes), in H2O, and in D2O were determined with an accuracy of about 1 MHz. The results are compared with those obtained from high-resolution ESR on H in H2O, and D in D2O, and in different silsesquioxanes in the temperature range 40–300 K. Both the strong isotope effect and the temperature dependence are well described by a single-oscillator model of Roduner et al. (J. Chem. Phys. 102 (1995) 5989). Striking differences seen between the different silsesquioxanes and between the porous Optipur and bulk Suprasil reflect varying spatial constraints and electronic interactions.

In order to provide an assessment of the “global” accuracy of the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential surface for H3, hot atom reaction yields, which are determined from collision processes over an energy range much wider than that of single-collision experiments, have been calculated for the Mu*+H2 and T*+H2 systems. The isotopic comparison of muonium (Mu=μ+e−), an ultralight isotope of hydrogen (mMu/mH≈1/9), with the heaviest H-atom isotope, tritium, is a novel approach in testing the global accuracy of the H3 surface. These reaction yields have been calculated using a formalism developed for (μ+) charge exchange, with input cross sections for elastic, inelastic (rovibrational excitation) and reactive collisions determined from quasi classical trajectories on the LSTH surface, in the center-of-mass energy range 0.5–11 eV. The rate of energy loss of the hot atom (Mu* or T*) due to elastic and inelastic collisions with the moderator (H2) drastically affects the hot atom reaction yield. In parti...

The rate constant of the gas-phase addition reaction of the light hydrogen isotope muonium to molecular oxygen, Mu + O2 → MuO2, was measured over a range of temperatures from 115 to 463 K at a pressure of 2 bar and from 16 to 301 bar at room temperature, using N2 as the moderator gas. The reaction remains in the termolecular regime over the entire pressure range. At room temperature, the average low-pressure limiting rate constant is kch0(Mu) = (8.0 ± 2.1) × 10-33 cm6 s-1, a factor of almost 7 below the corresponding rate constant for the H + O2 addition reaction, kch0(H). In contrast to kch0(H), which exhibits a clear negative temperature dependence, kch0(Mu) is essentially temperature independent. At room temperature, the kinetic isotope effect (KIE) is strongly pressure (density) dependent and is reversed at pressures near 300 bar. The kinetics are analyzed based on the statistical adiabatic channel model of Troe using a Morse potential, which works well in reproducing the overall KIE. The major factor...

The thermal reaction Mu + N2O has been studied by the muon spin rotation (μSR) technique at temperatures from 303 to 593 K and pressures up to 60 atm. The overall reaction rate coefficient depends ...

Muon spin rotation (μSR) and avoided level crossing resonance (ALCR) have been used to determine the hyperfine coupling constants (hfcs) of the muonium-substituted cyclohexadienyl radicals C6H6Mu, C6D6Mu and C6F6Mu in the gas phase, at pressures ∼1 and 15 atm and temperatures in the range 40–80°C. Equivalent studies of polyatomic free radicals in gases, by electron spin resonance (ESR) spectroscopy, are generally not possible in this pressure range. The present gas phase results support the findings of earlier studies of cyclohexadienyl radicals in the condensed phase, by both μSR and ESR. Minor but not insignificant (∼1%) effects on the hfcs are observed, which can be qualitatively understood for such nonpolar media in terms of their differing polarizabilities. This is the first time that comparisons of this nature have been possible between different phases at the same temperatures. These μSR/ALCR gas-phase results provide a valuable benchmark for computational studies on radicals, free from possible effects of solvent or matrix environments.

The spin relaxation of Mu was measured in mixtures of CO and Ar at pressures up to 270 atm and at various magnetic fields. The relaxation rate increased with magnetic field in the way expected for electron spin‐exchange processes, though the effect declined at high pressures. We describe the results in terms of spin relaxation of Mu‐formyl radicals, MuCO, which break up to give depolarized Mu at low pressures, but are increasingly stabilized at higher pressures.

The spin relaxation of the muonium‐substituted ethyl radical (MuCH2ĊH2) and its deuterated analog (MuCD2ĊD2) has been studied in the gas phase in both transverse and longitudinal magnetic fields spanning the range ∼0.5–35 kG, over a pressure range from ∼1–16 atm at ambient temperature. The Mu13CH213ĊH2 radical has also been investigated, at 2.7 atm. For comparison, some data is also reported for the MuCH2Ċ(CH3)2 (Mu‐t‐butyl) radical at a pressure of 2.6 atm. This experiment establishes the importance of the μSR technique in studying spin relaxation phenomena of polyatomic radicals in the gas phase, where equivalent ESR data is sparse or nonexistent. Both T1 (longitudinal) and T2 (transverse) μSR relaxation rates are reported and interpreted with a phenomenological model. Relaxation results from fluctuating terms in the spin Hamiltonian, inducing transitions between the eigenstates assumed from an isotropic hyperfine interaction. Low‐field relaxation is primarily due to the electron, via both the nuclear h...

Chemisorption of muonium onto the surface of gold nanoparticles has been observed. Muonium (μ+e−), a light hydrogen-like atom, reacts chemically with uncapped 7 nm gold nanoparticles embedded in mesoporous silica (SBA-15) with a strong temperature-dependent rate. The addition rate is fast enough to allow coherent spin transfer into a diamagnetic muon state on the nanoparticle surface. The muon is well established as a sensitive probe of static or slowly fluctuating magnetic fields in bulk matter. These results represent the first muon spin rotation signal on a nanoparticle surface or any metallic surface. Only weak magnetic effects are seen on the surface of these Au nanoparticles consistent with Pauli paramagnetism.

Rates for the gas‐phase thermal reaction Mu+CH4→MuH+CH3 (Mu=μ+e−), have been measured using the μSR (muon spin rotation) technique, over the temperature range 625–820 K. A good fit is obtained to the usual Arrhenius expression, k=A exp(−Ea/RT), giving an activation energy Ea=24.6±0.9 kcal/mol, ∼12 kcal/mol higher than that of the H‐atom isotopic variant of this reaction, H+CH4→H2+CH3. This Ea difference is the largest yet seen at high temperatures between H and Mu in the gas phase, and seems much too high to be explained in terms of [zero‐point‐energy (ZPE)] differences in their respective transition states, indicating instead a dramatic difference in reaction dynamics. The possible sources of this difference include differing reactivities from vibrationally excited states and/or a more favorable tunneling path for the H+CH4 reaction due to its suspected much earlier (and thinner) reaction barrier. In contrast, the similar H‐atom abstraction reactions with H2 and C2H6 gave Ea differences which matched expectations based on ZPE shifts, suggesting a qualitative difference in dynamics between these otherwise homologous reactions. It is suggested that reaction from vibrationally excited states may be relatively more important in the case of the Mu+CH4 reaction.

Muonium (Mu=μ + +e - ) is the bound state of a positive muon and an electron. Since the positive muon has a mass about 1/9 of the proton, Mu can be regarded as an ultra light isotope of hydrogen with unusually large mass ratios (Mu:H:D:T=1/9:1:2:3). The muon spin rotation technique (μSR) relies on the facts that (1) the muon produced in pion decay, π + →μ + +ν μ , is 100% spin polarized and (2) the positron from muon decay is emitted preferentially along the instantaneous muon spin direction at the time of the muon decay. In transverse field μSR (TF-μSR), the precession of the muon spin in muonium substituted radicals is directly observed by detecting decay positrons time differentially. From observed radical frequencies, the hyperfine coupling constants (A μ ) of C 2 H 4 Mu, C 2 D 4 Mu, 13 C 2 H 4 Mu, C 2 F 4 Mu, and C 2 H 3 FMu are determined. In the longitudinal field avoided level crossing (LF-ALC) technique, one observes the resonant loss of the muon spin polarization caused by the crossing of hyperfine levels at particular magnetic fields. The LF-ALC method together with the information on A μ obtained from TF-μSR allows one to determine the magnitude and sign of the nuclear hyperfine constants at α- and β-positions. Results are compared with hydrogen substituted ethyl-radicals and isotope effects are discussed

It has been shown experimentally that the muonium relaxation due to spin exchange is 1.5 times faster in intermediate transverse fields (say, atB=50 G, where the so-called two-frequency muonium signal is observed) than in low fields (say, atB=5 G), in agreement with an earlier theoretical prediction. It has also been confirmed experimentally that this distinct field dependence is totally absent in the case of chemical reaction.

Thermal reaction rates for the gas-phase reaction Mu+C2H6→MuH+C2H5 have been measured byμSR over the temperature range 510–730 K. The usual Arrhenius expression,k=Aexp(−E a /RT), fits the data well, giving parametersA=1.0×10−9 cm3 molecule−1 s−1 andE a =15.35 kcal/mol. The activation energyE a is 5.5 kcal/mol higher than for the H atom variant of this reaction, indicating a marked difference in reaction dynamics. Preliminary analysis indicates a still greater difference between Mu and H for the corresponding CH4 reaction.

Evidence for the formation of NeMu*, an isotopic analog of the Rydberg molecule NeH*, has been obtained from the observation of chemiluminescent emission in the near‐infrared region. This is the first spectroscopic detection of a muonium‐containing molecule. NeMu* was formed by stopping a 4 MeV muon (μ+) beam in a target vessel containing 1–6 atm of Ne and ∼1 Torr Ar. The wavelength spectrum of the emission, from ∼680–1000 nm, was measured using a variable‐wavelength filter, with a resolution of ±12.5 nm. Lower resolution spectra were also taken with a series of long pass filters. A complete histogram of photon events vs time was collected for each wavelength. Two strong transitions are observed, centered at 818 and 943 nm. Identification of NeMu* was made by a comparison of the experimental spectrum with a simulated spectrum based on detailed ab initio calculations, extended to higher excitation levels than had heretofore been reported. Both experimental and theoretical results are reported here. Althoug...

Reported here is the first μSR study of the muon (A(μ)) and proton (A(p)) β-hyperfine coupling constants (Hfcc) of muoniated sec-butyl radicals, formed by muonium (Mu) addition to 1-butene and to cis- and trans-2-butene. The data are compared with in vacuo spin-unrestricted MP2 and hybrid DFT/B3YLP calculations reported in the previous paper (I), which played an important part in the interpretation of the data. The T-dependences of both the (reduced) muon, A(μ)′(T), and proton, A(p)(T), Hfcc are surprisingly well explained by a simple model, in which the calculated Hfcc from paper I at energy minima of 0 and near ±120° are thermally averaged, assuming an energy dependence given by a basic 2-fold torsional potential. Fitted torsional barriers to A(μ)′(T) from this model are similar (~3 kJ/mol) for all muoniated butyl radicals, suggesting that these are dominated by ZPE effects arising from the C−Mu bond, but for A(p)(T) exhibit wide variations depending on environment. For the cis- and trans-2-butyl radicals formed from 2-butene, A(μ)′(T) exhibits clear discontinuities at bulk butene melting points, evidence for molecular interactions enhancing these muon Hfcc in the environment of the solid state, similar to that found in earlier reports for muoniated tert-butyl. In contrast, for Mu−sec-butyl formed from 1-butene, there is no such discontinuity. The muon hfcc for the trans-2-butyl radical are seemingly very well predicted by B3LYP calculations in the solid phase, but for sec-butyl from 1-butene, showing the absence of further interactions, much better agreement is found with the MP2 calculations across the whole temperature range. Examples of large proton Hfcc near 0 K are also reported, due to eclipsed C−H bonds, in like manner to C−Mu, which then also exhibit clear discontinuities in A(p)(T) at bulk melting points. The data suggest that the good agreement found between theory and experiment from the B3LYP calculations for eclipsed bonds in the solid phase may be fortuitous. For the staggered protons of the sec-butyl radicals formed, no discontinuities are seen at all in A(p)(T), also demonstrating no further effects of molecular interactions on these particular proton Hfcc.

The neutral muonic helium atom may be regarded as the heaviest isotope of the hydrogen atom, with a mass of ~4.1 atomic mass units ((4.1)H), because the negative muon almost perfectly screens one proton charge. We report the reaction rate of (4.1)H with (1)H(2) to produce (4.1)H(1)H + (1)H at 295 to 500 kelvin. The experimental rate constants are compared with the predictions of accurate quantum-mechanical dynamics calculations carried out on an accurate Born-Huang potential energy surface and with previously measured rate constants of (0.11)H (where (0.11)H is shorthand for muonium). Kinetic isotope effects can be compared for the unprecedentedly large mass ratio of 36. The agreement with accurate quantum dynamics is quantitative at 500 kelvin, and variational transition-state theory is used to interpret the extremely low (large inverse) kinetic isotope effects in the 10(-4) to 10(-2) range.

The thermally averaged total electron spin-flip cross sections ([sigma][sub SF]) for Mu-Cs have been measured in a 2 atm N[sub 2] moderator at 543, 566, and 643 K using the muon-spin-rotation technique. Within an overall experimental error of [plus minus]15%, the measured cross sections can be taken as temperature independent, [sigma][sub SF]=39.7[plus minus]6.0[times]10[sup [minus]16] cm[sup 2], though there may be a trend to decreased values at the lower temperatures. This average value is considerably lower than either the early calculated results of Dalgarno and Rudge [Proc. R. Soc. London Ser. A 286, 519 (1965)] or the more recent ones of Cole and Olson [Phys. Rev. A 31, 2137 (1985)] for the corresponding H-Cs collisions, indicating a dramatic isotope effect.

Gas-phase {mu}SR studies of dense methane up to 10 mol L{sup {minus}1} and of propane at low densities, up to 0.2 mol L{sup {minus}1}, are reported. It is found that the diamagnetic polarization, P{sub D}, increases in both gases with pressure, with a related decrease seen in the muonium polarization, P{sub Mu}. The initial increase seen in P{sub D} at low densities is attributed to hot-atom (Mu*) abstraction and substitution reactions. Comparisons with both hot-tritium (T*) and epithermal H* reactions in the alkanes reveal substantial isotope effects. In the case of CH{sub 4}, a continued increase in P{sub D} at higher densities is likely due to a proton-transfer reaction from the molecular ion CH{sub 4}Mu{sup +} in the radiolysis track, forming CH{sub 3}Mu, rather than to hot-atom reactions. Extrapolation of the present trend with density gives agreement with the value of P{sub D} found in liquid CH{sub 4}, indicating that the diamagnetic muon polarization in dense alkanes depends primarily on density rather than on temperature or phase.

The reaction rates of the muonium (Mu) atom with HBr and HI in ∼1 atm N2 moderator have been measured over the temperature range 160–490 K using the μSR technique. While both abstraction and exchange reactions are possible, only the abstraction reaction should be observable, being moderately exothermic. Comparisons with the corresponding H(D) reactions reveal small kinetic isotope effects in both reactions, which do not vary strongly with temperature (kMu/kH≊3.5 near 300 K), consistent with the (classical) ratio of mean velocities. Surprisingly, quantum tunneling, normally facile for similarly exothermic reactions of the ultralight Mu atom (mMu/mH≊1/9), appears to be of little importance here. This despite the fact that the (temperature‐independent) experimental activation energies are much less than the expected vibrationally adiabatic barrier heights (estimated to be ≊1.5 kcal mol−1) and, particularly in the case of Mu+HI, much less than the corresponding H‐atom activation energy: 0.13±0.03 vs 0.70±0.3 ...

The chemical reaction of interest, from the field of μSR spectroscopy, is that of the muonium atom (Mu) with molecular hydrogen in its first vibrational excited state. The stimulated Raman pumping (SRP) technique has been used to prepare H2 in its ν = 1 state in a series of off-line experiments at the LASIR Lab at UBC. Three different SRP excitation schemes employing the second harmonic of a Nd:YAG laser have been analysed in connection with this application, for 5.5, 13, and 26 cm-long reaction cells. The laser energy varied from ∼80 to ∼550 mJ/pulse (or from ∼0.07 GW/cm2 to ∼0.46 GW/cm2) at a 10 Hz repetition rate. The importance of injection seeding of the Nd:YAG laser for efficient molecular excitation is shown. The major challenge of this experiment was to ensure a homogeneous excitation over a large volume (few cm3) while achieving a high amount of vibrationally excited H2 (3-15 Torr). This is demanded by the requirements of superposition of a pulsed muon beam with the laser beam and the expected rate constant of the Mu + H2*(ν=1) MuH + H reaction. In this endeavour it was also of interest to explore the effect of added moderator gas to the hydrogen and so the effect of Ar/Xe moderator on the efficiency of hydrogen pumping for different SRP excitation schemes is also shown. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Gas-phase {mu}SR studies of dense methane up to 10 mol L{sup {minus}1} and of propane at low densities, up to 0.2 mol L{sup {minus}1}, are reported. It is found that the diamagnetic polarization, P{sub D}, increases in both gases with pressure, with a related decrease seen in the muonium polarization, P{sub Mu}. The initial increase seen in P{sub D} at low densities is attributed to hot-atom (Mu*) abstraction and substitution reactions. Comparisons with both hot-tritium (T*) and epithermal H* reactions in the alkanes reveal substantial isotope effects. In the case of CH{sub 4}, a continued increase in P{sub D} at higher densities is likely due to a proton-transfer reaction from the molecular ion CH{sub 4}Mu{sup +} in the radiolysis track, forming CH{sub 3}Mu, rather than to hot-atom reactions. Extrapolation of the present trend with density gives agreement with the value of P{sub D} found in liquid CH{sub 4}, indicating that the diamagnetic muon polarization in dense alkanes depends primarily on density rather than on temperature or phase.

A new model is developed for the analysis of muon spin relaxation (μSR) measurements of muonium (Mu) reaction rates with other chemical species. The kinetics component of the model is specifically developed for addition reactions but can be extended to direct reactions. The polarization component of the model assumes that the adduct formed possesses a single, effective spin precession frequency. The complete model is solved to obtain an analytic expression for the μSR signal as a function of time. Both a time‐ordered sequence method and a Boltzmann spin equation method give equivalent solutions. These solutions are analyzed under various kinetic conditions. It is concluded that the coefficient controlling the decay of the μSR signal is closely related to the adduct formation rate constant, i.e., the high pressure limit of the apparent bimolecular addition rate constant. In the most favorable case, the decay constant gives the adduct formation rate constant directly at all pressures of buffer gas.

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.

Results of the first μSR studies using Merck FO Optipur silica powder, which contains paramagnetic impurities at the ppb level and has a surface area of 610±20 m2/g. are reported. Above 20 K, the transverse field muonium relaxation rate is roughly constant at 0.5 μs−1. Upon the addition of oxygen at ppm levels, the relaxation rate increases linearly with O2 concentration in the temperature range from 40–100 K yielding two-dimensional depolarization rate constants on the order of 10−4 cm2 molecule−1 s−1. As the temperature is increased further, both oxygen and muonium desorb from the surface yielding a three-dimensional rate constants at 300 K of 3.1(3)×10–10−10 cm3 molecule−1 s−1, in agreement with the gas phase value. Longitudinal field measurements suggest that MuO2 is formed and is able to spin exchange with other oxygen molecules.

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.

The phase information of triplet muonium signals has been used to measure the slowing down times of the positive muon in Ar. The results agree well with calculated stopping power based on proton data with the assumption that the positive muon and proton have the same stopping power at the same projectilew velocity (velocity scaling).

Results of muon polarization studies in xenon and argon up to 60 atm are reported. In argon for pressures up to 10 atm, the muon polarization is best explained by an epithermalcharge exchange model. Above this pressure, the decrease inP D and increase inP L are ascribed to charge neutralization and spin exchange reactions, respectively, in the radiolysis track. Measurements with Xe/He mixtures with a xenon pressure of 1 atm indicate that the lost polarization in the pure xenon at this pressure is due to inefficient moderation of the muon. As the pressure in pure xenon is increased above 10 atm, we find thatP L remains roughly constant andP D begins to increase. The lost fraction may be due to the formation of a XeMu Van der Waals type complex, whileP D is ascribed to XeMu+ formation. This suggests that spur processes appear to be less important in xenon than in argon.

Muon polarizations are reported for nitrogen and ethane over a wide pressure range from below 1 to 200 atm for N2 and up to 245 atm for C2H6. The N2 measurements were made at ambient temperature, while those for C2H6 were made at temperatures both above and below the critical temperature (305.3 K). This is the first μSR study of muonium and diamagnetic muon formation to cover the entire range from a low pressure gas to densities typical of liquids. The data are discussed in terms of hot atom and spur models. In the lowest pressure range, below 1.5 atm for N2 and about 10 atm for C2H6, the muonium polarization increases with pressure. This is well understood in terms of epithermal charge exchange. In N2 there is a small diamagnetic fraction, which is ascribed to the N2Mu+ molecular ion. This fraction approaches zero as the pressure is increased to 200 atm, with a corresponding increase in the muonium fraction, consistent with charge neutralization of the molecular ion by electrons from the radiolysis track...

Rate constants have been measured for the reaction of the light hydrogen isotope muonium with benzene and 2,3-dimethylbutadiene-1,3 in the gas phase and in several solvents. Comparison with H atom data reveals (1) appreciable kinetic isotope effects, (2) a strong contribution of tunnelling for the activated reaction with benzene, (3) encounter controlled reaction for Mu addition to the diene, (4) a mass dependence of the diffusion constant of hydrogen isotopes in solution, and (5) an enhancement of the rate constant in solution over that in the gas phase by a factor, except for water, of the inverse Ostwald solubility coefficient for hydrogen. The isotope-dependent reduction of the solvent effect in water is tentatively ascribed to the dynamics of the clathrate-like structure when the hydrogen atom reacts.

The reaction kinetics for the addition of the muonium (Mu=μ+e−) atom to C2H4 and C2D4 have been measured over the temperature range 150–500 K at (N2) moderator pressures near 1 atm. A factor of about 8 variation in moderator pressure was carried out for C2H4, with no significant change seen in the apparent rate constant kapp, which is therefore taken to be at the high pressure limit, yielding the bimolecular rate constant kMu for the addition step. This is also expected from the nature of the μSR technique employed, which, in favorable cases, gives kapp=kMu at any pressure. Comparisons with the H atom data of Lightfoot and Pilling, and Sugawara et al. and the D atom data of Sugawara et al. reveal large isotope effects. Only at the highest temperatures, near 500 K, is kMu/kH given by its classical value of 2.9, from the mean velocity dependence of the collision rate but at the lowest temperatures kMu/kH≳30/1 is seen, reflecting the pronounced tunneling of the much lighter Mu atom (mμ=1/9 mp). The present M...

The times taken by positive muons $({\ensuremath{\mu}}^{+})$ to slow down from initial energies in the range $\ensuremath{\sim}3$ to $1\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$, to the energy of the last muonium formation, $\ensuremath{\approx}10\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, at the end of cyclic charge exchange, have been measured in the pure gases ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, $\mathrm{Ar}$, and in the gas mixtures $\mathrm{Ar}\text{\ensuremath{-}}\mathrm{He}$, $\mathrm{Ar}\text{\ensuremath{-}}\mathrm{Ne}$, $\mathrm{Ar}\text{\ensuremath{-}}{\mathrm{CF}}_{4}$, ${\mathrm{H}}_{2}\text{\ensuremath{-}}\mathrm{He}$, and ${\mathrm{H}}_{2}\text{\ensuremath{-}}{\mathrm{SF}}_{6}$, by the muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ technique. At $1\phantom{\rule{0.3em}{0ex}}\mathrm{atm}$ pressure, these slowing-down times, ${\ensuremath{\tau}}_{\mathrm{SD}}$, in $\mathrm{Ar}$ and ${\mathrm{N}}_{2}$, vary from $\ensuremath{\sim}14\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ at the highest initial energies of $2.8\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ to $6.5\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ at $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$, with much longer times, $\ensuremath{\sim}34\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, seen at this energy in ${\mathrm{H}}_{2}$. Similar variations are seen in the gas mixtures, depending also on the total charge and nature of the mixture and consistent with well-established (Bragg) additivity rules. The times ${\ensuremath{\tau}}_{\mathrm{SD}}$ could also be used to determine the stopping powers, $dE∕dx$, of the positive muon in ${\mathrm{N}}_{2}$, $\mathrm{Ar}$, and ${\mathrm{H}}_{2}$, at kinetic energies near $2\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. The results demonstrate that the ${\ensuremath{\mu}}^{+}$ and proton have the same stopping power at the same projectile velocity, as expected from the historic Bethe-Bloch formula, but not previously shown experimentally to our knowledge for the muon in gases at these energies. The energy of the first neutralization collision forming muonium (hydrogen), which initiates a series of charge-exchanging collisions, is also calculated for $\mathrm{He}$, $\mathrm{Ne}$, and $\mathrm{Ar}$. The formalism necessary to describe the stopping power and moderation times, for either muon or proton, in three energy regimes---the Bethe-Bloch, cyclic charge exchange, and thermalization regimes---is developed and discussed in comparison with the experimental measurements reported here, and elsewhere. The slowing-down times through the first two regimes are controlled by the relevant ionization and charge-exchange cross sections, whereas the final thermalization regime is most sensitive to the forwardness of the elastic scattering cross sections. In this regime the slowing-down times (to $kT$) at nominal pressures are expected to be $\ensuremath{\lesssim}100\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.

The room-temperature termolecular rate constants, k0, for the Mu + CO + M==MuCO + M (M = He, N2, Ar) recombination reaction have been measured by the muSR technique, and are reported for moderator gas pressures of up to approximately 200 bar (densities less, similar 0.4 x 10(22) molec cm(-3)). The experimental relaxation rates reveal an unusual signature, in being dominated by the electron spin-rotation interaction in the MuCO radical that is formed in the addition step. In N2 moderator, k0 = 1.2+/-0.1 x 10(-34) cm(6) s(-1), only about 30% higher than found in Ar or He. The experimental results are compared with theoretical calculations carried out on the Werner-Keller-Schinke (WKS) surface [Keller et al., J. Chem. Phys. 105, 4983 (1996)], within the framework of the isolated resonance model (IRM). The positions and lifetimes of resonance states are obtained by solving the complex Hamiltonian for the nonrotating MuCO system, using an L2 method, with an absorbing potential in the asymptotic region. Accurate values of the vibrational bound and resonance states of MuCO reveal unprecedented isotope effects in comparisons with HCO, due to the remarkable effect of replacing H by the very light Mu atom (m(Mu) approximately (1/9)m(H)). Due to its pronounced zero-point energy shift, there are only two (J = 0) bound states in MuCO. Contributions from nonzero J states to the termolecular rate constants are evaluated through the J-shifting approximation, with rotational constants evaluated at the potential minimum. The value of the important A constant (181 cm(-1)) used in this approximation was supported by accurate J = K = 1 calculations, from which A = 180 cm(-1) was obtained by numerical evaluation. The calculations presented here, with a "weak collision factor" beta c = 0.001, indicative of the very sparse density of MuCO states, give a very good account of both the magnitude and pressure dependence of the experimental rates, but only when the fact that the two initially bound (J = 0) states become resonances for J0 is taken into account. This is the first time in IRM calculations of atom-molecule recombination reactions where J not equal to 0 states have proven to be so important, thus providing a truly unique test of quantum rate theory.

This paper reports on the experimental background and methodology leading to recent results on the first accurate measurement of the reaction rate of the muonium (Mu) atom from a state-selected reactant in the gas phase: the Mu + H2 MuH + H reaction at 300 K, and its comparison with rigorous quantum rate theory, Bakule et al (2012 J. Phys. Chem. Lett. 3 2755). Stimulated Raman pumping, induced by 532 nm light from the 2nd harmonic of a Nd:YAG laser, was used to produce H2 in its first vibrational (v = 1) state, H, in a single Raman/reaction cell. A pulsed muon beam (from ‘ISIS’, at 50 Hz) matched the 25 Hz repetition rate of the laser, allowing data taking in equal ‘Laser-On/Laser-Off’ modes of operation. The signal to noise was improved by over an order of magnitude in comparison with an earlier proof-of-principle experiment. The success of the present experiment also relied on optimizing the overlap of the laser profile with the extended stopping distribution of the muon beam at 50 bar H2 pressure, in which Monte Carlo simulations played a central role. The rate constant, found from the analysis of three separate measurements, which includes a correction for the loss of concentration due to collisional relaxation with unpumped H2 during the time of each measurement, is = 9.9[(−1.4)(+1.7)] × 10−13 cm3 s−1 at 300 K. This is in good to excellent agreement with rigorous quantum rate calculations on the complete configuration interaction/Born–Huang surface, as reported earlier by Bakule et al, and which are also briefly commented on herein.

We report muon spin rotation/relaxation measurements of muonium in mesoporous silica (SBA-15) with a high specific surface area of 600 m2/g. Up to 70 percent of the incoming muons form muonium and escape efficiently into the open pores at all temperatures between 3 and 300K. We present evidence that the interaction with the silica surfaces involves both spin exchange and a transition to a diamagnetic state, possibly due to dangling bonds on the surface. At very low temperatures, below 20K, the interaction between muonium and the silica surfaces is suppressed due to a He film coating the surfaces. These results indicate that it should be possible to use muonium to probe the surfaces of uncapped nanoparticles supported in silica.