Mu Atoms Research Articles

Comment on “Role of the transition state in muon implantation” and “Thermal spike in muon implantation”

Vil\~ao et al. (Phys. Rev. B 96, 195205 (2017) and Phys. Rev. B 99, 195206 (2019)) have reported positive muon spin rotation/relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) experiments on various insulating metal oxides, solar cell materials, and alloyed Ge. They note the presence of a separate early component in the ${\ensuremath{\mu}}^{+}$ polarization time dependence which relaxes more rapidly than the longer lived signal and also exhibits (in ${\mathrm{ZrO}}_{2}$:Mg) a slightly increased frequency at low temperature in transverse field. They interpret this early component as a weakly bound ``transition state'' of the neutral muonium ($\mathrm{Mu}={\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$) atom formed epithermally by the incoming 4-MeV muon, in which the hyperfine interaction between the muon and the electron is ``motionally narrowed'' by rapid spin exchange, resulting in a ``diamagneticlike'' Larmor precession signal. This ``diamagneticlike transition state'' supposedly takes microseconds to relax into its final ground state due to the reluctance of the surrounding lattice to deform around the Mu atom. However, numerous earlier experiments (including those in electric fields) on various liquids and solids ranging from wide-gap insulators to narrow-gap semiconductors have convincingly shown that Mu formation proceeds through capture of radiolysis electrons by thermalized muons---a process crucially dependent on the electron mobility rather than epithermal dynamics. Therefore, we question the validity of the interpretation by Vil\~ao et al. and raise some important issues that need clarification.

Theoretical study on anomalous kinetic isotope effects in H/Mu addition to pyrazine: Effects of water microsolvation in solution kinetics

Previous experimental studies have shown that addition of H and Mu atoms to pyrazine in aqueous solution leads to different reaction products. H adds to the N atom of the pyrazine ring, whereas Mu adds preferentially to the C atom. In this work, to explain this anomalous isotope effect, we performed reaction path analyses for the H/Mu+pyrazine·(H2O)n (n=0–2) reactions at the density functional theory level by considering microsolvation effects. Without water microsolvation, the barrier height of the addition to N is always lower than that of the addition to C. However, the barrier height of the addition to N is slightly higher than that of the addition to C when the N atom of the pyrazine ring is pre-solvated by water through an N⋯H−O hydrogen bond. Thermal rate constants are calculated within a variational transition state theory framework including quantum tunneling corrections and are compared with the experimental results.

Isotope Dependence and Quantum Effects on Atomic Hydrogen Diffusion in Liquid Water.

Relative diffusion coefficients were determined in water for the D, H, and Mu isotopes of atomic hydrogen by measuring their diffusion-limited spin-exchange rate constants with Ni(2+) as a function of temperature. H and D atoms were generated by pulse radiolysis of water and measured by time-resolved pulsed EPR. Mu atoms are detected by muonium spin resonance. To isolate the atomic mass effect from solvent isotope effect, we measured all three spin-exchange rates in 90% D2O. The diffusion depends on the atomic mass, demonstrating breakdown of Stokes-Einstein behavior. The diffusion can be understood using a combination of water "cavity diffusion" and "hopping" mechanisms, as has been proposed in the literature. The H/D isotope effect agrees with previous modeling using ring polymer molecular dynamics. The "quantum swelling" effect on muonium due to its larger de Broglie wavelength does not seem to slow its "hopping" diffusion as much as predicted in previous work. Quantum effects of both the atom mass and the water librations have been modeled using RPMD and a qTIP4P/f quantized flexible water model. These results suggest that the muonium diffusion is very sensitive to the Mu versus water potential used.

First accurate experimental study of Mu reactivity from a state-selected reactant in the gas phase: the Mu + H2{1} reaction rate at 300 K

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.

Accurate Prediction of Hyperfine Coupling Constants in Muoniated and Hydrogenated Ethyl Radicals: Ab Initio Path Integral Simulation Study with Density Functional Theory Method.

We performed ab initio path integral molecular dynamics (PIMD) simulations with a density functional theory (DFT) method to accurately predict hyperfine coupling constants (HFCCs) in the ethyl radical (CβH3-CαH2) and its Mu-substituted (muoniated) compound (CβH2Mu-CαH2). The substitution of a Mu atom, an ultralight isotope of the H atom, with larger nuclear quantum effect is expected to strongly affect the nature of the ethyl radical. The static conventional DFT calculations of CβH3-CαH2 find that the elongation of one Cβ-H bond causes a change in the shape of potential energy curve along the rotational angle via the imbalance of attractive and repulsive interactions between the methyl and methylene groups. Investigation of the methyl-group behavior including the nuclear quantum and thermal effects shows that an unbalanced CβH2Mu group with the elongated Cβ-Mu bond rotates around the Cβ-Cα bond in a muoniated ethyl radical, quite differently from the CβH3 group with the three equivalent Cβ-H bonds in the ethyl radical. These rotations couple with other molecular motions such as the methylene-group rocking motion (inversion), leading to difficulties in reproducing the corresponding barrier heights. Our PIMD simulations successfully predict the barrier heights to be close to the experimental values and provide a significant improvement in muon and proton HFCCs given by the static conventional DFT method. Further investigation reveals that the Cβ-Mu/H stretching motion, methyl-group rotation, methylene-group rocking motion, and HFCC values deeply intertwine with each other. Because these motions are different between the radicals, a proper description of the structural fluctuations reflecting the nuclear quantum and thermal effects is vital to evaluate HFCC values in theory to be comparable to the experimental ones. Accordingly, a fundamental difference in HFCC between the radicals arises from their intrinsic molecular motions at a finite temperature, in particular the methyl-group behavior.

New results for the formation of a muoniated radical in the Mu + Br2 system: a van der Waals complex or evidence for vibrational bonding in Br–Mu–Br?

New evidence is presented for the observation of a muoniated radical in the Mu + Br(2) system, from μSR longitudinal field (LF) repolarisation studies in the gas phase, at Br(2) concentrations of 0.1 bar in a Br(2)/N(2) mixture at 300 K and at 10 bar total pressure. The LF repolarisation curve, up to a field of 4.5 kG, reveals two paramagnetic components, one for the Mu atom, formed promptly during the slowing-down process of the positive muon, with a known Mu hyperfine coupling constant (hfcc) of 4463 MHz, and one for a muoniated radical formed by fast Mu addition. From model fits to the Br(2)/N(2) data, the radical component is found to have an unusually high muon hfcc, assessed to be ∼3300 MHz with an overall error due to systematics expected to exceed 10%. This high muon hfcc is taken as evidence for the observation of either the Br-Mu-Br radical, and hence of vibrational bonding in this H[combining low line]-L[combining low line]-H[combining low line] system, or of a MuBr(2) van der Waals complex formed in the entrance channel. Preliminary ab initio electronic structure calculations suggest the latter is more likely but fully rigorous calculations of the effect of dynamics on the hfcc for either system have yet to be carried out.

Similarity of Primary Processes in Tracks of Fast Electrons, Positrons, Muons and in Blobs of Moessbauer Atoms. Common Model of early Chemical Reactions for Radiation, Positron, Muon Chemistry and Moessbauer Spectroscopy

A unified mechanism describing formation of Ps and Mu atoms in condensed matter, radiolytic hydrogen in water and products of Auger ionization in Moessbauer atoms is presented. All these processes are similar to the Ps formation mechanism in a condensed molecular milieu.

The muonic He atom and a preliminary study of the reaction

The muonic atom He4μ has the composition α++μ-e-, and is formed by stopping negative muons in He doped with a small amount of NH3 (or Xe). It may be regarded as a unique heavy H-atom isotope with a mass of 4.1 amu. As such, the study of its chemical reaction rates and comparison with those of the well-known light Mu atom (0.113 amu) allows unprecedented tests of kinetic isotope effects over a range of 36 in mass. As a first example, and one which is of most fundamental interest, we have begun kinetics studies of the Heμ+H2→HeμH+H reaction in the gas phase. The first measurements, at 295 K, give a rate constant of kHeμ=4.1±0.7×10-16cm3molec-1s-1. In comparison, variational transition state calculations give a value of 2.46×10-16cm3molec-1s-1, somewhat below the measurement, despite the large error bar, raising the possibility that the calculations, on an essentially exact potential energy surface, have underestimated the amount of quantum tunneling involved, even for this heavy H-atom isotope.

Magnetic properties of CoNRhMnanoparticles: experiment and theory

The magnetism of Co-Rh nanoparticles is investigated experimentally and theoretically. The particles (approximately 2 nm) have been synthesized by decomposition of organometallic precursors in mild conditions of pressure and temperature, under hydrogen atmosphere and in the presence of a polymer matrix. The magnetic properties are determined by SQUID, Mössbauer spectroscopy, and X-ray magnetic circular dichroism (XMCD). The structural and chemical properties are characterized by wide angle X-ray scattering, transmission electronic microscopy and X-ray absorption near edge spectroscopy. All the studied Co-Rh clusters are magnetic with an average spin moment per atom mu that is larger than the one of macroscopic crystals or alloys with similar concentrations. The experimental results and comparison with theory suggest that the most likely chemical arrangement is a Rh core, with a Co-rich outer shell showing significant Co-Rh mixing at the interface. Measured and calculated magnetic anisotropy energies (MAEs) are found to be higher than in pure Co clusters. Moreover, one observes that the MAEs can be tuned to some extent by varying the Rh concentration. These trends are well accounted for by theory, which in addition reveals important spin and orbital moments induced at the Rh atoms as well as significant orbital moments at the Co atoms. These play a central role in the interpretation of experimental data as a function of Co-Rh content. A more detailed analysis from a local perspective shows that the orbital and spin moments at the Co-Rh interface are largely responsible for the enhancement of the magnetic moments and magnetic anisotropy.

Theoretical rate constants and kinetic isotope effects in the reaction of methane with H, D, T, and Mu atoms

The rate constants and kinetic isotope effects of the reaction of methane with four isotopes of hydrogen, protium (H), deuterium (D), tritium (T), and muonium (Mu), were studied using variational transition state theory with multidimensional tunneling on an analytical potential energy surface, PES-2002, previously constructed by our group. For the four isotopes, our kinetics results agree reasonably with available experimental measurements, improving previous theoretical results that used different potential energy surfaces and/or theoretical approaches. In the comparison of the reactivity between protium and muonium, which is the most severe test of the surface and theoretical method due to the large mass difference between the two isotopes, some sources of discrepancy between theory and experiment were analyzed. These were the zero-point energy, tunneling effect, and the role of the reactivity from methane excited vibrational states.

Theoretical study of the H + Br 2 and Mu + Br 2 reactions: A new ab initio potential energy surface and quantum dynamics calculations

A new global potential energy surface for the H + Br 2 → HBr + Br reaction has been developed at the MRCI+Q/aug-cc-pVTZ ab initio level of theory. It has been found that this level calculation gives a negative barrier slightly below the H + Br 2 reactant energy level. Time-dependent and time-independent quantum dynamics calculations have been performed on this potential energy surface. The calculated cumulative reaction probabilities for J = 0 around the reaction threshold energy region show a very similar behavior for both the H + Br 2 and Mu + Br 2 reaction, in qualitative disagreement with experimental measurements, where a positive activation energy was observed for the H + Br 2 reaction while a negative activation energy for the Mu + Br 2 reaction. Variational calculations of vibrational energy levels have also been performed to study dynamical vibrational bonding for the Br–Mu–Br molecule. It has been found that the system has several vibrational bonding states, whose wave functions are localized around the transition-state of the Br + MuBr′ → MuBr + Br′ exchange reaction, below the lowest Br + MuBr asymptotic energy level. This result qualitatively supports the recent experimental finding that a long-lived radical containing a Mu atom is produced in the Mu + Br 2 reaction.

Termolecular kinetics for the Mu+CO+M recombination reaction: A unique test of quantum rate theory

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 J > 0 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.

Muonium in InSb: Shallow acceptor versus deep trap or recombination center

The bound state of a muonium atom has been detected in both $n$-type and $p$-type InSb using a high-field $\ensuremath{\mu}\mathrm{SR}$ technique. The hyperfine constant obtained for this isotropic center $({A}_{\mathrm{T}}=2464\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$, roughly half that of a Mu atom in vacuum, is characteristic of deep level ${\mathrm{Mu}}^{0}$ centers at tetrahedral interstitial sites in other cubic semiconductors, which typically ionize above $250\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In contrast, the ${\mathrm{Mu}}^{0}$ signal in InSb begins to disappear near $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is more characteristic of ionization of a shallow level impurity. The charge-state dynamics of Mu in InSb can be understood in terms of the predicted shallow acceptor behavior for H in InSb versus a deep hole trap or recombination center, rather than as ionization via electron promotion to the conduction band.

Quantum diffusion of muonium atoms in solids: Localization vs. band-like propagation

Studies of muonium dynamics in insulators and semiconductors at low temperature have led to two fundamentally different pictures: Mu is found to localize strongly in Van der Waals crystals, while in alkali halides and compound semiconductors it has long been believed to undergo bandlike propagation with a characteristic bandwidth Δ ∼ 0.1 K . Our recent measurements in transverse field indicate that Mu atom may be localized at low temperatures in both KCl and GaAs. This apparent discrepancy with previous results may dramatically change our understanding of muonium quantum dynamics in solids, raising the question of whether Mu atoms can ever be truly delocalized at low temperature or if its localization is a general phenomenon in solids.

Excess electron transport in cryoobjects

Experimental results on excess electron transport in solid and liquid phases of Ne, Ar, and solid N2–Ar mixture are presented and compared with those for He. The muon spin relaxation technique in frequently switching electric fields was used to study the phenomenon of delayed muonium formation: excess electrons liberated in the μ+ ionization track converge upon the positive muons and form Mu (μ+e−) atoms. This process is shown to be crucially dependent upon the electron’s interaction with its environment (i.e., whether it occupies the conduction band or becomes localized in a bubble of tens of angstroms in radius) and upon its mobility in these states. The characteristic lengths involved are 10−6–10−4 cm, and the characteristic times range from nanoseconds to tens of microseconds. Such a microscopic length scale sometimes enables the electron to spend its entire free lifetime in a state which may not be detected by conventional macroscopic techniques. The electron transport processes are compared in: liquid and solid helium (where the electron is localized in a bubble); liquid and solid neon (where electrons are delocalized in the solid, and the coexistence of localized and delocalized electron states in the liquid was recently found); liquid and solid argon (where electrons are delocalized in both phases); orientational glass systems (solid N2–Ar mixtures), where our results suggest that electrons are localized in an orientational glass. This scaling from light to heavy rare gases enables us to reveal new features of excess-electron localization on a microscopic scale. Analysis of the experimental data makes it possible to formulate the following tendency of the muon end-of-track structure in condensed rare gases. The muon–self-track interaction changes from isolated-pair (muon plus the nearest track electron) in helium to multipair (muon in the vicinity of tens of track electrons and positive ions) in argon.

Coherent tunnelling dynamics of muonium in a disordered medium

Conventional understanding suggests that strong disorder inevitably causes particle localization: states with the same energy are too far apart in space for tunnelling to be effective. We present experimental evidence to the contrary: we have observed coherent tunnelling of Mu atoms in a highly disordered mixture—75% CH 4+25% Kr—which forms an orientational glass phase at low temperatures.

Solvation and kinetic isotope effects in H and D abstraction reactions from formate ions by D, H and Mu atoms in aqueous solution

Electron paramagnetic resonance free induction decay attenuation and muon spin rotation measurements were performed in the temperature range of liquid water for the reactions of the hydrogen isotopes D, H, and Mu with undeuterated and deuterated formate ions. Accurate rate constants were determined, and excellent Arrhenius behavior represented by was found in all cases. Ab initio calculations at the MP2 and the QCISD level with the aug-cc-pvDZ basis set reveal that the reaction has no electronic barrier in the gas phase. This contrasts with quite sizeable activation energies observed in aqueous solution, and it suggests that the barrier is entirely solvent induced. Calculations at the above mentioned ab initio level using a polarized dielectric continuum for the solvated reaction system restore a realistic barrier and confirm this interpretation. It is shown that the solvent effect is a consequence of a pronounced change of polarization of the system along the reaction path. It may be more appropriate to describe the reaction as a consecutive electron–proton transfer rather than an H atom abstraction.

Electron transport in cryocrystals

We review our recent experimental studies of the excess electron transport in cryocrystals and cryoliquids. We use a muon spin relaxation technique to explore the phenomenon of delayed muonium formation: excess electrons liberated in the μ+ ionization track converge upon the positive muons and form Mu (μ+e−) atoms in which the μ+ polarization is partially lost. The spatial distribution of such electrons with respect to the moon is shown to be highly anisotropic: the μ+ thermalizes well “downstream” from the center of the electron distribution. Measurements in electric fields up to 30 kV/cm allow one to estimate the characteristic muon-electron distance in different insulators: the results range from 10−6 cm to 10−4 cm. This circumstance makes the basis of a recently developed new technique for electron transport studies on microscopic scale: electron mobility can be extracted when both the characteristic muon-electron distance and characteristic time for muonium atom formation are determined. The microscopic length scale enables the electron to sometimes spend its entire free lifetime in a state which may not be detected by conventional macroscopic techniques. The muonium formation process in condensed matter is shown to depend critically upon whether the excess electron forms a polaron or remains in a delocalized state. Different mechanisms of electron transport in insulators are discussed.

The addition reaction of X to O2 (X = Mu, H, D): isotope effects in intra- and intermolecular energy transfer

Rate constants are calculated for the addition reaction of the light hydrogen isotope muonium (Mu) to oxygen and compared with the analogous additions of H and D and with experimental results. The origin and magnitude of kinetic isotope effects is discussed. Both the pressure dependence and the temperature dependence in different pressure regimes are analysed with the goal to check the applicability of statistical reaction theories to these systems. Two different theories are applied. One is based on approximations as introduced by Troe (J.Chem.Phys., 1977, 66, 4758; J.Phys.Chem., 1979, 83, 114; and J.Phys.Chem., 1981, 75, 226), while in the second one, the master equation is solved numerically. The microcanonical rate constants going into the master equation are calculated using RRKM theory, and for the activation/deactivation as a consequence of collisions with moderator (N2), an exponential energy transfer mechanism is assumed. Comparison with low pressure experiments leads to the conclusion that collisions of the moderator with highly excited MuO2* molecules are much less efficient than those with HO2*, as far as activation/deactivation is concerned. This result may be explained by the larger vibrational frequencies of MuO2*. The linear dependence with the moderator concentration of the Mu rate constants up to 300 bar, as observed in the experiment, could partly be simulated, but some discrepancy remains. In this context, the possibility of non-RRKM behaviour is discussed. Finally, the major influence of tunneling, especially for the light Mu atom, is analysed. It is suggested that the effect of tunneling near the low pressure limit may exceed significantly its high pressure limiting value.

A proposed study on trapping of positive muon in defects in the vicinity of metal surfaces

We aim to reveal the dynamics of positive muon ( μ +) trapping in the vicinity of metal surfaces through the precise measurement of trapping rates during muon thermal diffusion in metals. This trapping strongly dominates the time evolution of the muonium atom (Mu: μ + e −) emitted to vacuum from the surface, since it is the positive muon reaching the surface within its lifetime (∼ 2.2 μs) that contributes to Mu emission in vacuum. In order to pursue the trapping rate on the order of ≈ 10 −1 μs −1, statistics of ≈ 10 −7 Mu atoms in vacuum would be needed, and use of the UT-MSL/KEK (Meson Science Laboratory, University of Tokyo, located at National Laboratory for High Energy Physics, Japan) and/or RIKEN-RAL (RIKEN-Rutherford Appleton Laboratory muon facility, UK) would facilitate obtaining these statistics within a reasonable time.