Quadrupole moment of muonium and hyperfine structure of muonium levels in silicon

It is shown that experimental data on Mu¹ in silicon are most satisfactorily described by the uniaxial symmetric spin hamiltonian which means muonium displacement from the octa-cell center.     

Preliminary calculations confirming that anomalous muonium in diamond and silicon is bond-centered interstitial muonium

The model of anomalous muonium as bond-centered interstitial muonium has been examined by approximate ab-initio Hartree-Fock calculations in diamond and silicon and found to be in excellent agreement with experiment.     

Muons and muonium in cryocrystals

We present a collection of measurements of the muon and muonium asymmetries and relaxation parameters in cryocrystals of N₂, CO, Xe,¹³⁶Xe and Ne as functions of temperature. Generally, the fractions of the two species can be attributed to a competition between the formation of muonium or a diamagnetic species, where processes involving transport of spur electrons are important.     

Current trends in muonium chemistry

As “rapporteur” for the papers submitted to this conference in the general area of muonium chemistry, I briefly review the major developments since μSR86, and attempt to show how the papers presented at μSR90 relate to each other and work published in the intervening years. Some topics are discussed in more detail than others, reflecting my own interests and views on what is of current importance. Nevertheless, I try to cover all current research in muonium chemistry. The major areas are: early events following muon thermalization, including subsequent loss of muon polarization (the “missing fraction”); molecular structure and dynamics, primarily of muonium-substituted free radicals: and reaction kinetics.     

Muon/muonium surface interactions

The interactions of muonium (μ ⁺ e ⁻, Mu) with the surfaces of fine silica powders have been extensively studied using zero, longitudinal and transverse field μSR techniques. These studies indicate diffusion and trapping behavior of the Mu atoms on the silica surface, which is strongly influenced by the surface hydroxyl (OH) concentration. Specifically, the presence of the surface OH groups is observed to inhibit the surface mobility of the Mu atoms at low temperatures. Information provided by zero and longitudinal field data suggest a random anisotropic distortion of the Mu hyperfine interaction (RAHD) as the principal relaxation mechanism. A recently developed RAHD spin relaxation theory is used to interpret these data. Additional investigations, using platinum loaded silica, have yielded the first observed surface reaction of Mu. Studies of the interactions of positive muons with surfaces have been also extended to single crystals, where low energy (<10 eV)μ ⁺ andMu ⁻ ions are observed to be reemitted from some materials (e.g., the <100> surface of lithium fluoride). Future applications of these emission phenomena toward the development of a slow^847-3 (or Mu⁻) beam are considered.     

Hydrogen and muonium in silicon

First principles calculations of the properties of hydrogen and muonium in silicon are presented. H⁺ and H⁻ are shown to have definite preferences for bond-centred and tetrahedral interstitial sites respectively whereas H⁰ (or a muon) is shown to be stable at two sites with almost equal energies, the bond-centred and antibonding sites. The structures of normal and isotropic muonium are discussed. In contrast to common belief the tetrahedral site is shown to be unstable with the muon moving spontaneously towards one of the neighbouring silicon atoms. The barrier to motion between equivalent antibonding sites is low suggesting that the normal muonium signal is isotropic because of motional averaging, not due to the symmetry of a well defined equilibrium site.     

Diamagnetic muonium states in InP

Transverse and zero‐field muon spin relaxation reveal several diamagnetic muonium states in InP characterized by their static linewidths and diffusion properties. We tentatively associate low‐temperature diamagnetic states with Mu⁺ in the BC and T_P interstitial sites and a missing fraction with Mu⁰ rapidly diffusing through T_In interstices. Trapping peaks above 250 K imply static centers which depend on doping type, consistent with Mu^- at T_In for n‐type samples and Mu coupled with a dopant or other defect for p‐type. This revised version was published online in August 2006 with corrections to the Cover Date.     

Observation of epithermal 2S muonium

A slow muon beam was passed through a thin aluminium foil and the emerging beam was studied for the presence of muonium in the 2S state. The fraction and the velocity distribution of the 2S muonium was determined.     

Formation of muonium substituted free radicals

SR experiments with mixtures of benzene with cyclohexane, 2,3-dimethyl-1,3-butadiene and carbontetrachloride allow the conclusion that the direct muonic precursor of the muonic cyclohexadienyl radical is thermal muonium. In neat benzene it has a life time of 10 ps and disappears by the addition reaction. Muonium is formed within about 1 ps by combination of the positive muon with an electron near the end of the track of the thermalizing muon.Support by the Swiss National Foundation for Scientific Research and by the Swiss Institute for Nuclear Research (SIN) are gratefully acknowledged.     

Recent results in muonium solution kinetics

Using Muonium Spin Rotation (MSR) techniques the aqueous solution kinetics of several muonium addition reactions and spin conversion interactions have been studied. The addition reactions show both diffusion and activation-controlled reaction rates with isotope effects between 1 and 3 for diffusion-control and between 7 and 31 for activation-control reactions. Barrier energies are typically 15 kJ/mole and 30 kJ/mole, respectively, for these processes in water. Spin-conversion interactions involving Ni_(aq ⁺² and Ni(cyclam)⁺² complexes showed that spin-conversion of triplet Mu by a paramagnetic solute occurs at or near the diffusion-controlled limit while the chemical reaction with the diamagnetic configuration of Ni(cyclam)⁺² occured some 100 times slower at k_M 5×10⁸M^–1s^–1.     

Inhomogeneous muonium diffusion in solid nitrogen

The spin dynamics of the muonium (Mu) atom diffusing quantum mechanically in solid nitrogen (s-¹⁴N₂) has been studied using the technique of Mu spin relaxation. A strong relationship between longitudinal (T ₁ ^–1 ) and transverse (T ₂ ^–1 ) relaxation rates (familiar in NMR) has been experimentally demonstrated for the first time for muonium relaxation. At low temperatures the results are inconsistent with diffusion models using a single correlation time _c; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate _c ^–1 gives clear evidence that Mu quantum diffusion ins-N₂ is governed by the two-phonon interaction.     

Dynamics of gas-phase reactions of muonium

Applications of variational transition state theory with semiclassical adiabatic transmission coefficients to the reactions of muonium with H₂, D₂, F₂, and Cl₂ are reviewed. In addition new calculations are presented for the Mu+Cl₂ and Br₂ reactions. The comparison of calculated rate constants and kinetic isotope effects (KIE's) with experiment is used as a test of the validity of semiempirical potential energy surfaces. Furthermore the VTST-plus-tunneling calculations allow an analysis of the KIE's that identifies those features of the potential which control the isotope effects.     

Quantum diffusion of muonium in insulators

In this paper we review our recent experiments conducted at TRIUMF on muonium diffusion in alkali halides. First, the technique of longitudinal-field muonium spin relaxation (T ₁) due to nuclear hyperfine interaction, an indispensabletour de force for the present work. is described. It is demonstrated in KCl that the technique provides spectacular sensitivity for muonium diffusion as well as determining the average nuclear hyperfine coupling constant. The muonium hop rate shows a minimum (T ^*≃80 K) and steep increase with decreasing temperature. The result is compared with the current theory of quantum diffusion in non-metallic crystals. A few more sets of new data may be presented for other alkali halides. In addition, we show that muonium forms a delocalized state in NaCl as evidenced by a large change of the average nuclear hyperfine parameter. Related topics of local tunneling system may be briefly reviewed.