Muon States Research Articles

Relaxation of muonium states in solids.

The dipole interaction between a muon, which forms a paramagnetic state in a solid, and neighboring nuclei leads to a relaxation of the hyperfine oscillations which are observed in transverse magnetic field experiments. It is shown how the damping rates, which depend on the superhyperfine interaction and the strength and orientation of the external field, can be calculated. An explicit expression for the relaxation function of anomalous muonium is derived which is valid for high fields and negligible quadrupole interactions. The determination of the muon site in the general case and the realxation function of normal muonium are discussed.

Muonium states in zincblende-structured compounds

The authors present a list of results of μSR experiments in materials with the diamond and zincblende structure. Besides the muonium hyperfine parameters, additional information is tabulated: the formation probability for the different muon states, the highest temperatures at which muonium states have been observed and the types of transitions found to occur between these states. The muonium hyperfine parameters show a linear rise as a function of host ionicity from Ge to GaAs to ZnSe followed by a sharp drop to CuBr.

Muonium in bulk fused quartz: Test case for RAHD relaxation theory

Muonium (μ + e −) in bulk fused quartz is a unique system in that theμ + spin polarization (in the muonium state) relaxes almost entirely via random anisotropic hyperfine distortions (RAHD). As such, this system provides an excellent test case for a new RAHD spin relaxation theory. This theory is quantitatively compared to static zero field data and the functional characteristics in both the high field and dynamic limits are considered as well.

Muonium states in silicon carbide

Implanted muons in samples of silicon carbide have been observed to form paramagnetic muonium centers (μ+ e−). Muonium precession signals in low applied magnetic fields have been observed at 22 K in a granular sample of cubic β-SiC, however it was not possible to determine the hyperfine frequency. In a single crystal sample of hexagonal 6H-SiC, three apparently isotropic muonium states were observed at 20 K and two at 300 K, all with hyperfine frequencies intermediate between those of the isotropic muonium centers in diamond and silicon. No evidence was seen of an anisotropic muonium state analogous to the Mu* state in diamond and silicon.

Longitudinal field quenching studies in KCl and KBr — Evidence for a precursor muonium state

The repolarization of μ+ in a longitudinal field as a function of field strength has been measured at various temperatures in KCl and KBr single crystals. The data at room temperature in KCl are essentially in agreement with Ivanteret al. /1/ and Nishiyamaet al. /5/. The obtained quenching curves can be reasonably fitted by assuming that the long lived muonium state, seen directly in transverse field experiments by Kieflet al. /4/, is preceded by another short lived muonium state with reduced hf-coupling. It is also necessary to allow for electron spin exchange in the precursor state. The model fits yield the hyperfine frequency of the precursor state, its chemical lifetime and an electron spin flip rate. It is speculated that the precursor state and the temperature dependence of the fitted parameters reflect the early history of the μ+ in its terminal spur.

Repolarization of negative muons by polarized 209Bi nuclei.

A large $\mu^-$ polarization was achieved in muonic Bi atoms with the help of the strong hyperfine field in a polarized nuclear target. Using $^{209}$Bi nuclei polarized to ($59\pm9$)% in ferromagnetic BiMn, we observed a $\mu$-$e$ decay asymmetry of ($13.1\pm3.9$)%, which gives $\mu^-$ polarization per nuclear polarization equal to $-1.07\pm 0.35$. This value is almost consistent with $-0.792$ calculated for nuclei with spin $I= \frac{9}{2}$ and a positive magnetic moment under the assumption that the hyperfine interaction becomes effective in the lowest muonic states.

Muonium to diamagnetic muon conversion in KCl and NaCl revealed by time-differential muon spin resonance

The conversion of muonium into a diamagnetic muon state in KCl and NaCl was directly observed by detecting a time-delayed appearance of diamagnetic muon states with muon spin resonance. The conversion rate, determined from the time-differential resonance signals, shows a thermal activation characteristic in temperature variation.

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).

Observation of “decoupled” diamagnetic muon states in Alkali halides by muon spin resonance

The states of positive muons in KCl, NaCl and KI were studied with the muon spin resonance method under a 3 kG decoupling longitudinal field, revealing a considerably larger fraction of diamagnetic muon state than observed by the conventional spin rotation method. The origin of this fraction, which increases with temperature, is attributed to a muonium to muon transition in solids.

Erratum: Muon states in uniaxially strained iron

Erratum: Muon states in uniaxially strained iron

Muon states in uniaxially strained iron

Muon states in uniaxially strained iron

Formation of Muonium in the2SState and Observation of the Lamb Shift Transition

Muonium in the 2S state has been produced by the beam foil method with a ..mu../sup +/ beam of 10 MeV/c. The metastable 2S state of muonium has been detected by a static--electric field quenching method, and the transition 2S/sub 1/2/, F = 1..-->..2P/sub 1/2/, F = 1 induced by a radio-frequency electric field has been observed with an event rate of about 4/h.

The effect of radiation defects in silicon single crystal lattice on the characteristic states of the interstitial muonium atom

Radiation defects are shown experimentally to affect differently the normal and anomalous muonium states in silicon. This evidences essentially different mobilities of the two muonium states in the sample lattice.

The transition from Mu to Mu* in diamond

Evidence is presented for a transition from the isotropic muonium state (Mu) to the [111] axially symmetric anomalous muonium state (Mu*) in diamond. Amplitude measurements for Mu* in a powder in zero field and with a single crystal oriented in a magnetic field indicate that such a transition occurs with a temperature-dependent rateΛ(T) and that the electron polarization is conserved during the transition. The possibility of determining the absolute sign of the Mu* hyperfine parameters is discussed.

Electronic structure and hyperfine interaction of muonium in semi-conductors

The Unrestricted Hartree-Fock self-consistent field cluster procedure is being utilized for first-principle investigations of the electronic structures and hyperfine interactions in normal and anomalous muonium states in semi-conductors. Our results for the total energy for the normal muonium state for a twenty-seven atom cluster in diamond, including the muonium and its neighboring atoms, show a minimum at the tetrahedral site and a maximum at the hexagonal site indicating that normal muonium is located in the tetrahedral region and avoids the hexagonal region. Using the calculated spin-density as a function of the position of muonium and carrying out averaging over the vibrational motion of the muon governed by the total energy curve obtained from our work, we have derived a muon hyperfine constant which is about 75% of that in free muonium, in good agreement with experiment. The natures of the total energy and spindensity curves permit us to draw conclusions regarding the origin of the observed trend in the hyperfine constants for normal muonium in diamond, silicon and germanium. The UHF cluster procedure is also applied to study a model of a muon in a positively charged environment for the anomalous muonium center in diamond. This model leads to a hyperfine interaction tensor with the observed feature of strong anisotropy but significantly weaker than experiment. The results obtained for this model indicate the importance for the anomalous muonium state with its relatively weak hyperfine interaction, of exchange polarization effects inherent in the UHF procedure.

Muon states in metals: Recent progress

We report on our results in two interesting questions related to muon spin rotation studies in condensed matter: (i) energetics of muons in metals, including lattice relaxation and zero point motion in self-trapping phenomena, and (ii) systematics of Knight shifts and hyperfine fields.

Theμ + state under decoupling field observed by spin resonance method in CS2, water and benzene

The muon spin resonance method was applied to measure theμ+ polarization corresponding to the muon state in diamagnetic compounds in CS2, water and benzene under 3 kG decoupling field. We observed almost the same diamagnetic polarizations under decoupling field, compared to those at zero decoupling field observed under the transverse field, except in CS2 The results indicate that most of the so called “missing fraction” is not associated with diamagnetic species produced as a final state of rapid chemical reactions of muonium in these samples.

Electron irradiation effects on muonium states in silicon

Normal and anomalous muonium were studied in electron irradiated silicon. We found that the two muonium states behave very differently: For normal muonium, the relaxation rate increases if the sample is irradiated whereas it decreases for anomalous muonium. Possible explanations for these processes are discussed.

Experimental Test of Higher-Order QED and a Search for Excited Muon States

The reactions e+e−→μ+μ−γγ and e+e−→μ+μ−γ have been studied at s=29 GeV with the MAC detector at the SLAC storage ring PEP. The measured cross sections, charge asymmetry, and invariant-mass distributions are in good agreement with the predictions of QED theory. Limits are derived for the production of excited muon states.Received 6 December 1982DOI:https://doi.org/10.1103/PhysRevLett.51.257©1983 American Physical Society

Negative-norm states, superselection rules, and the lepton family

Field theories containing states of both positive and negative norm are considered. With the correct definition of the number operators for the quantum fields, all physical quantities are rendered canonically normalized. If the theory admits a global symmetry leading to a superselection rule which forbids transitions between positive- and negative-norm states, then the negative-norm states are allowed to be physical. Specifically, a spinor theory with higher-order field equations and multiple excitations is considered and applied to the charged lepton system: $e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$. In this model, the negative norm of the muon state allows us to understand the nonexistence of $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ decay. For minimal coupling, the theory is renormalizable and equivalent to three separate fermion electrodynamics with the additional prediction of equal charge for the leptons. A further anomalous magnetic moment coupling can only allow one of the decays $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ or $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$.