Muon States Research Articles

Muon radical states in some electron donor and acceptor molecules

Muon radical states were studied in the electron donor molecules TTF and BEDT-TTF and in the electron acceptor molecule TCNQ. Muonium addition to double bond carbon sites results in hyperfine coupling contants ranging from 350 MHz in TTF down to 80 MHz for TCNQ. In TTF and BEDT-TTF additional radical states with extremely low hyperfine coupling constants in the 5 MHz region are observed; these are assigned to muon addition at sulphur sites accompanied by C — S bond cleavage. Copyright © 2000 John Wiley & Sons, Ltd.

Novel Muonium State in CdS

A new type of muonium defect center has been observed in undoped CdS below 20 K. The hyperfine interaction amounts only to approximately ${10}^{\ensuremath{-}4}$ of the vacuum value, and is shown to have axial symmetry along the Cd-S bond direction. Results suggest that the muon is close to the sulfur antibonding site and the paramagnetic electron density is distributed over a large volume. In contrast to the behavior in other semiconductors, muonium forms a shallow center in CdS. By implication, analog isolated hydrogen impurity atoms act as electrically active shallow-level defect centers in CdS.

Negatively charged muonium states in gallium nitride

Muon nuclear-quadrupole level-crossing resonances (QLCR) and zero-field muon spin depolarization functions are identified for negatively charged muonium (Mu−) centers in wurtzite-structured GaN.The QLCR spectra imply that Mu− occupies interstitial locations next to Ga atoms, consistent with the two inequivalent Ga anti-bonding sites. Mu− related depolarization shows an increase in average dipolar fields near 200K and indicates motion above 500K. Transitions suggested by relaxation features are briefly discussed.

First-principles study of the quantum states of muonium and hydrogen in crystalline silicon

We present a theoretical study of the quantum states of muonium and atomic hydrogen in crystalline silicon using the generalized gradient approximation to density-functional theory combined with the path-integral molecular-dynamics method. Normal muonium, one of the two stable states, is distributed around the tetrahedral site. The potential-energy surface is considerably modified in the presence of muonium by distorting silicon cage and stabilizes the state. The other state of muonium, anomalous muonium, is located around the bond center site with significant quantum vibration in a steep potential well. The relative stabilities and dynamics of the two sites are discussed, and the essential roles of quantum effects are emphasized.

A search for invisible Higgs bosons produced in e+e− interactions at LEP 2 energies

Searches for HZ production with the Higgs boson decaying into an invisible final state have been performed with the data collected by the DELPHI experiment up to the centre-of-mass energy of 183 GeV. The hadronic and muon pair final states of the Z boson were analysed. From the absence of signal, upper limits on the cross-section and the corresponding Higgs boson mass limits were set at 95% confidence level. The results are interpreted as excluded parameter regions in the framework of the minimal supersymmetric standard model and in the simplest Majoron model with one Higgs doublet and one Higgs singlet field.

Muonium formation via electron transport in solid nitrogen

Muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ techniques have been used to investigate the diamagnetic and paramagnetic states of energetic positive muons stopped in solid molecular nitrogen. The paramagnetic signal arises from muonium $(\mathrm{Mu}\mathrm{}={\ensuremath{\mu}}^{+}{+e}^{\ensuremath{-}})$ atoms and reflects both ``prompt'' epithermal Mu formation and ``delayed'' thermal Mu formation. The latter is shown to be due to convergence of the thermalized ${\ensuremath{\mu}}^{+}$ with an electron liberated in its ionization track. Measurements in external electric fields of up to 10 kV/cm applied along and antiparallel to the initial muon momentum reveal a large anisotropy in the spatial distribution of muon-electron pairs: the ${\ensuremath{\mu}}^{+}$ is shown to thermalize ``downstream'' of the ionization products of its track. The characteristic muon-electron distances in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{N}}_{2}$ and $\ensuremath{\beta}\ensuremath{-}{\mathrm{N}}_{2}$ and liquid nitrogen are estimated to be approximately 500 \AA{}, 250 \AA{}, and 300 \AA{}, respectively. The dependence of delayed Mu formation upon electron mobility offers a method for determining such mobilities on a microscopic scale. Electron drift mobilities are shown to differ by several orders of magnitude in the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases of solid nitrogen. Excess electrons from the muon track are apparently delocalized in orientationally ordered $\ensuremath{\alpha}\ensuremath{-}{\mathrm{N}}_{2};$ electron localization in orientationally disordered $\ensuremath{\beta}\ensuremath{-}{\mathrm{N}}_{2}$ is discussed in terms of the formation of a small polaron due to electron interaction with the rotational degrees of freedom of ${\mathrm{N}}_{2}$ molecules. The diamagnetic signal in condensed nitrogen is ascribed to the ${\mathrm{N}}_{2}{\ensuremath{\mu}}^{+}$ molecular ion; in $\ensuremath{\beta}\ensuremath{-}{\mathrm{N}}_{2}$ it consists of two components, one relaxing slowly due to random fields from nuclear dipole moments and the other relaxing up to two orders of magnitude faster, due to very delayed Mu formation as the muon captures low-mobility electrons.

Recent results from the search by CHORUS for νμ → ντ oscillations

Results from the search for ν μ → ν τ oscillations by CHORUS are presented. Some of the data collected in 1994–1996 have been analysed, searching for ν τ charged current interactions followed by the decay of the τ lepton into a negative hadron or into a muon. Neutrino interaction vertices have been located in the emulsion target for 69,056 events with an identified final state muon and 7,206 events without an identified muon. Within the applied cuts, no ν τ candidate has been found. This result leads to a 90% C.L. limit P( ν μ → ν τ ) < 6.0·10 −4 on the mixing probability.

Dynamics of negative muonium inn-type silicon

Temperature-dependent diamagnetic amplitudes from radio-frequency muon spin-resonance data on two moderately to heavily doped n-type silicon samples require the presence of ${\mathrm{Mu}}_{T}^{\ensuremath{-}}.$ We determine the ${\mathrm{Mu}}_{T}^{\ensuremath{-}}$ to ${\mathrm{Mu}}_{T}^{0}$ ionization energy to be $0.56\ifmmode\pm\else\textpm\fi{}0.03 \mathrm{eV}$ for silicon, considerably higher than the ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$ to ${\mathrm{Mu}}_{\mathrm{BC}}^{+}$ ionization energy of $0.21\ifmmode\pm\else\textpm\fi{}0.01 \mathrm{eV}.$ Thus muonium will be a negative-$U$ impurity only if the energy difference between the ${\mathrm{Mu}}_{T}^{0}$ and ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$ configurations is less than 0.35 eV. The $\mathrm{Mu}(0/+)$ thermodynamic level correlates well with results for monatomic hydrogen, but the $\mathrm{Mu}(\ensuremath{-}/0)$ level is estimated to be shallower than that claimed for $\mathrm{H}(\ensuremath{-}/0).$ The muonium data show a complicated set of transitions active during the muon lifetime, and involving four separate muonium states. Similar rapid transitions should be considered when interpreting data on isolated hydrogen centers.

High Precision Measurements of the Ground State Hyperfine Structure Interval of Muonium and of the Muon Magnetic Moment

High precision measurements of two Zeeman hyperfine transitions in the ground state of muonium in a strong magnetic field have been made at LAMPF using microwave magnetic resonance spectroscopy and a resonance line narrowing technique. These determine the most precise values of the ground state hyperfine structure interval of muonium $\ensuremath{\Delta}\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4463302765(53)\mathrm{Hz}$ $(12\mathrm{ppb})$, and of the ratio of magnetic moments ${\ensuremath{\mu}}_{\ensuremath{\mu}}/{\ensuremath{\mu}}_{p}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.18334513(39)$ $(120\mathrm{ppb})$, representing a factor of 3 improvement. Values of the mass ratio ${m}_{\ensuremath{\mu}}/{m}_{e}$ and the fine structure constant $\ensuremath{\alpha}$ are derived from these results.

Muon spin relaxation in double chain system KCuCl3

In muon spin relaxation studies on the S = 12 double chain system KCuCl3, which is thought to have a spin singlet ground state with a finite spin gap, we found that the muon spin becomes strongly depolarized below 20 K. Under a longitudinal magnetic field of 3800 G, the temperature dependence of the muon spin relaxation rate shows a cusp at ∼ 5 K, where the relaxation rate increases with increasing longitudinal magnetic fields, suggesting the existence of a frustrated spin state. We believe that the origin of the muon spin relaxation is related to the electron spins of the Cu2+ ions which form the doubie chains or formation of the paramagnetic muon state. Possible other reasons of the muon spin relaxation are also discussed.

Muon spin relaxation studies of interstitial and molecular motion

The unusual methods of preparation and analysis of spin polarization in μSR spectroscopy, which exploit the unique properties of the positive muon, are introduced in this article. Following a summary overview of applications, particular attention is paid to the problem of spin-lattice relaxation for a muon experiencing a hyperfine interaction with a single unpaired electron. The specific cases considered are the interstitial diffusion of muonium—the 1-electron atom which may be considered as a light isotope of hydrogen—and the molecular dynamics of organic radicals labelled by muonium. Rate equations for the evolution of population in the hyperfine-coupled spin states are solved numerically for various relaxation mechanisms. The formalism is equally valid for conventional ESR studies of paramagnetic states but is pursued specifically to simulate T 1-relaxation in μSR. The simulations are compared with literature data. Also treated is the case of intermittent hyperfine coupling, appropriate to electron capture and loss in semiconductors or soliton motion in polymers; for this, a Monte Carlo approach is used to simulate the muon response. (For low-dimensional motion, the relaxation function is not exponential, so that a unique value of T 1 cannot be defined.) Finally, a proposal is made to implement muon- T 1 ρ measurements in the rotating frame; this is designed for the selective study of electronically diamagnetic muonium states (i.e., those without hyperfine coupling) in the presence of a paramagnetic muonium or radical fraction.

All-Order Binding Corrections to Muonium Hyperfine Splitting

The use of exact Dirac-Coulomb propagators allows the evaluation of binding corrections to the Schwinger correction in ground state muonium hyperfine splitting to all orders. The calculational method is described and the results are used firstly to verify recent perturbative calculations of higher-order binding corrections and secondly to evaluate the residual terms of still higher order. Implications for muonium hyperfine splitting are discussed.

Muonium states and dynamics as a model for hydrogen in semiconductors

An atomistic picture of interstitial hydrogen in semiconductors involves, as it does for hydrogen in metals, determination of the lattice sites and configurations adopted and the mechanisms of diffusion. An additional dimension is added in semiconductors, namely the possibility of examining different charge states of the defect centre—positive, neutral and negative—respectively the diamagnetic proton, the paramagnetic hydrogen atom and diamagnetic hydride ion. Muon spectroscopy has been successful in modelling all these states, determining their local structure, their different stabilities, mobilities and interactions with charge carriers. In semiconductors doped heavily to metallic conductivities, only diamagnetic states are observed, though still with a rich variety of mobilities and trapping sites. Studies of the interaction and pairing with dopant atoms, simulating the important process of passivation, also appear promising. This short review is illustrated with recent results for the elemental semiconductors Si and Ge and the compounds GaAs and InP.

Implanted muon states in porous silicon

It is desirable to know the location and type of the hydrogen within the nanostructure of porous silicon (PS). Hydrogen is, however, very difficult to detect and locate with conventional spectroscopic techniques. The presence of hydrogen in bulk crystalline and amorphous silicon is well-known, and it can exist in the form of intrinsic hydrogen, implanted hydrogen or as an impurity. Muon studies of amorphous and bulk crystalline silicon suggest that there are two important states for muonium and hence hydrogen in silicon, termed the `normal' and `anomalous' sites. Normal muonium is generally described as being located at the centre of the tetrahedral cage site. The second state is anisotropic and is believed to lie at the centre of a stretched Si–Si bond. Here we report muon implantation of PS and this is discussed in terms of the nanostructure dimensionality.

Evidence for muonium passivation in n-doped Ge

Two different diamagnetic muon states have been identified through their response to bulk electronic excitation in crystalline n-type Ge: one, found above \ensuremath{\sim}100 K, rapidly charge exchanges with photogenerated carriers, while the other, seen at low temperatures, shows little or no such behavior. The electronic inactivity of the latter state (${\mathrm{Mu}}^{\mathrm{\ensuremath{-}}}$, produced by a slow charge-transfer reaction between muonium and an impurity donor atom) further suggests that the electronic level is located outside the energy-band gap, equivalent to ``muonium passivation'' of the donor.

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (MuT) and the diamagnetic states (μd), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (MuBC) and μd. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond.

Influence of doping admixture and anisotropic tension on behaviour of muon spin polarization in insulators

We investigate the model describing a muon tunneling between two equivalent positions in (magnetic) insulators. Crystals are assumed to have concentrations such that the muon tunneling states in a double well potential can be considered as real during the muon lifetime \tauμ. In the simplest model there are only two such states: the ground state and the first excited state. Our aim is to calculate lifetimes \tau1(T) and \tau0(T) of these muon tunneling states resulting from interaction between the muon and phonons of the sample. In the case of a distorted double well potential, all matrix elements of \hatĤ(ph)int are finite. This leads to rescaling of the first and second orders of the perturbation theory compared with the results for the muon in “pure” samples. We explain the vanishing of some part of the oscillation frequencies of the muon polarization vector in the framework of a muon‐phonon interaction model: for example, it is necessary to take into account that \tau1(T) decreases more rapidly than \tau0(T) when the temperature increases. If the muon tunnels through a set of equivalent interstitial positions in a unit cell, the experimental picture of the polarization vector behaviour can change drastically under the action of various strain fields.

Muonium states and dynamics in phosphorus and sulphur

The various states formed by positive muons implanted into phosphorus and sulphur have been characterized as a model for interstitial hydrogen, of which little is known in these elements. Repolarization studies reveal muonium‐like states in each case, giving estimates of the hyperfine parameters and, for sulphur at least, an indication of the coexistence of a molecular radical state. The longitudinal‐field relaxation functions suggest conversion of the paramagnetic states to diamagnetic, i.e. ionization or chemical reaction, in competition with strong spin–lattice relaxation.

ELECTRONIC STRUCTURE AND DYNAMICS OF MUONIUM IN SEMICONDUCTORS

In this paper, a selection of recent results on muonium in semiconductors is presented. These are primarily taken from Si and GaAs and encompass the electronic structure of the diamagnetic centers, charge state cycling, spin‐exchange scattering and interconversion between muonium states. These experiments illustrate the power of μSR for investigating the behavior of muonium and, by analogy, the technologically relevant isolated hydrogen centers in semiconductors.

Muon state dynamics in germanium and silicon

The dynamics of the various muon states (paramagnetic states muonium Mu and anomalous muonium Mu*, diamagnetic states μd) were studied by means of radio‐frequency μ+ spin resonance (RFμSR), longitudinal field‐quenching (LFQ), and transverse μ+ spin rotation (TFμSR) in an undoped high‐purity and a gallium‐doped germanium single crystal in the temperature range 3.5–320 K.