Muon level crossing resonance in niobium

A useful guide to detecting quadrupole level crossing resonance (QLCR) spectra is to search in the vicinity of B_E\cdot(\gamma_n/\gamma_μ), where B_E is the onset magnetic field for the decoupling of the quadrupole interaction, as seen in muon spin rotation linewidths. More detailed predictions of the positions and intensities of the resonances require numerical simulations taking account of the local geometry of the muon site. We present such simulations for muons adjacent to nuclei of spin 9/2 and demonstrate a pronounced dependence on the anisotropy of the quadrupole coupling tensor. Simulations for the specific cases of muons located at the octahedral and tetrahedral interstices in niobium metal are compared with the experimentally detected spectrum in a polycrystalline sample. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon level crossing resonance in diamagnetic systems-general considerations

This paper is a general discussion of the nature of the level crossing phenomena in diamagnetic systems, with particular emphasis on the quadrupolar LCR as evidenced in Cu. The system exhibits some surprises at higher temperatures which indicate that the level crossing technique contains hitherto unsuspected capabilities for μSR.     

Muon level crossing resonance of the R3NMu+ ion

Observation of muon level crossing resonance with¹⁴N nuclei in frozen triethylamine is reported and assigned to the ionic species (C₂H₅)₃NMu⁺. In forming this species, the implanted positive muons mimic the chemical behaviour of protons as usual, here in a process analogous to the protonation of a base. The resultant molecular ion has the axial symmetry necessary for detection of level crossing with an integral-spin nucleus. The quadrupole coupling constant is determined to be ¦e ² qQ/h¦=0.41(4) MHz, corresponding to an electric field gradient on¹⁴N of 0.10(1) a.u. and consistent with anab initio estimate for species of the type R₃NMu⁺. The prospects for detection of the muonium-substituted ammonium ion NH₃Mu⁺ ion in ammonia are discussed.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

Muon addition to nitrogen,oxygen and other atoms: Considerations for level crossing resonance studies

The purpose of this note is to examine the conditions under which muon level crossing resonance with quadrupolar nuclei may be used to characterise the elusive diamagnetic fraction which is formed when positive muons are stopped in various media and associated chemically with the host molecules. A potential difficulty is identified for nuclei having integral spin, which may explain why cross polarisation to¹⁴N has not yet been detected. The general suitability of nuclei with half-integral spin (I≥3/2) is illustrated with the case of¹⁷O, and suggestions are made for future studies with other nuclei, including species such as molecular ions and defect complexes (muon-impurity pairs).     

Radical reorientation dynamics studied by positive-muon avoided level crossing resonance

Spin polarised positive muons substituted for a hydrogen nucleus in organic radicals are used as spin labels to sense reorientational motion of the radicals in orienting environments. The effect of uniaxial motion on the spectrum of the muonated cyclohexadienyl radical in a benzene single crystal and of its hexamethyl derivative in polycrystalline hexamethylbenzene is demonstrated. Isotopic spectra for cyclohexadienyl radicals adsorbed on SiO₂ are explained by translational diffusion around the 7 nm grain. The potential of the technique to study transient radical intermediates of processes in heterogeneous catalysis is discussed.     

Muon level-crossing resonance in Si∶Al

A systematic investigation of five sherds from the Celtic oppidum of Manching by refiring in different atmospheres is presented. The data are part of an extended and general study of Celtic ceramics in early Europe.     

Muon level-crossing resonance in magnetically ordered materials

The positive muon is widely used as a microscopic probe of internal fields at interstitial sites in magnetically ordered materials. Recently, we have demonstrated that the hyperfine fields on the neighboring host nuclear spins can be measured using a novel muon level-crossing resonance technique, thus providing a more detailed picture of the electronic and magnetic environment around the muon. In this paper I will describe the fundamentals of muon level-crossing resonance as applied to magnetically ordered materials, and report an example in MnF₂.     

Muon spin resonance — A variant of magnetic resonance

Spin polarized positive muons injected in matter serve as magnetic probes for the investigation of various properties. The evolution of muon spin polarization rests on the same basis as in conventional magnetic resonance techniques. The background of the technique, different variants of the experimental set-up, and potential and limitations of the muon as a probe are described.     

Sphaleron and level crossing

We study the fermionic hamiltonian in the standard electroweak theory in the presence of a sphaleron. We show that there exists a normalizable solution of the zero energy Dirac equation. We explicitly calculate the zero mode using a simple variational ansatz for the sphaleron radial functions.     

Level crossing resonance in muonium-like systems

This paper describes the phenomenon of level crossing resonance (or avoided level crossing) encountered in paramagnetic systems involving a muon. Recent experiments on muonated radicals and muonium defect centers in semiconductors are reviewed which demonstrate how the technique provides detailed information on nuclear hyperfine structure, which is unresolvable with more standard techniques. The science implications are discussed.     

Level crossing mechanism in new coherence resonance

The mechanism of level crossing in the new coherence resonance for the case that a spin-$\text{1}\text{2}$ atom interacts with an oscillating rf field in optical pumping is theoretically analyzed considering the higher-order effects of a strong rf field.     

Born-oppenheimer approximation near level crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.     

Determination of the spin Hamiltonian constants for electron spin resonance at energy level crossing points

The crossing point of the Cr⁺³ ion energy-levels in single-crystal K₃Co(CN)₆, with the applied magnetic field parallel to the y-axis, is determined experimentally. Precisely calculated values of the constants E and D of the EPR spin Hamiltonian are shown to agree closely with those obtained by other authors.In conclusion, I wish to thank Professor V. S. Grechishkin for supervising my work and discussing the results.     

Rapid adiabatic passage without level crossing

We present a method for achieving complete population transfer in a two-state quantum system via adiabatic time evolution in which, contrary to conventional rapid adiabatic passage produced by chirped pulses, there occurs no crossing of diabatic energy curves: there is no sign change of the detuning. Instead, we use structured pulses, in which, in addition to satisfying conditions for adiabatic evolution, there occurs a sign change of the Rabi frequency when the detuning is zero. We present simulations that offer simple geometrical interpretation of the two-dimensional motion of the Bloch vector for this system, illustrating how both complete population inversion and complete population return occur for different choices of structured pulses.     

Quantum interferences at nuclear level crossing

Two nuclear hyperfine levels can cross when a quadrupole and magnetic interaction are combined. When the levels come close enough, interferences between two transitions can occur if coherence conditions are fulfilled. In this paper we discuss the possibility that coherence and interferences could occur if the zero fluctuations of an electromagnetic field in a crystal lattice would be anisotropic. This revised version was published online in August 2006 with corrections to the Cover Date.     

Competition between benzene and styrene in forming radicals under different solvent conditions observed by muon level crossing resonance

The muon level-crossing-resonance technique has been used to resolve major discrepancies that exist in muon-spin-resonance studies (both free-radical formation and muonium decay rates) in the competition between benzene and styrene. The results, obtained for 30 mM solutions in ethanol and for 2.5 mM aqueous micelles solutions, show that muonium atoms (Mu) react 8 (±2) times faster with styrene than with benzene. In the above cases thermalized Mu is unquestionably the reactive species, which is known to show nucleophilic intra-molecular selectivity in the case of styrene. But a similar value, 9 (±2), was also obtained for undiluted mixtures of liquid benzene and styrene (neat mixture) — where the precursor might have been hot Mu (which should display weaker selectivity than Mu) or cations derived from ⁺ (which should show higher selectivity). These results support the view that thermalized Mu is the predominant reactive species in liquid benzene and styrene.