The competition between kondo and RKKY interaction in CeTSn compounds

This article reviews our investigations of the series CeTSn where T stands for a transition element. Our research was stimulated by the unusual behavior of CeNiSn. These compounds are close to the border between magnetic and nonmagnetic Kondo systems. For the understanding of their physical properties a detailed knowledge of the magnetic properties is essential. μSR experiments allow one to reveal even weak magnetic correlations. Special attention is given to the explanation of experimental details. Pulsed (ISIS) and continuous (TRIUMF) muon beams were used as complementary techniques. Experiments in zero and longitudinal (with respect to the muon spin) applied field allowed the determination of the static width of the magnetic field distribution seen by the muons due to ionic moments as well as the fluctuation rate of the internal field. As a part of our experiments, the muon site has been determined and the procedure for this will be described.     

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.     

Aspects of the two-component and four-component neutrino theories in connection with weak lepton and semilepton processes

A comparison is made of the results found in the application of two-component and four-component theories of the two neutrinos to weak lepton processes (muon decay) and semilepton processes. The predictions of the two theories clearly differ in the V-A version of the coupling of electron and muon currents and of muon and baryon currents. In contrast with the theory of two-component neutrinos (the V-A interaction), four-component theory predicts that a V + A interaction of electron and muon currents is responsible for muon decay.     

Fundamental weak interaction studies using polarised nuclei and ion traps

Two experiments to search for new physics beyond the standard model for electroweak interactions by measuring correlations between different spin and momentum vectors in nuclear β-decay are discussed. In the first experiment the correlation between the emission asymmetry and the longitudinal polarisation of positrons emitted by polarised nuclei is determined. This type of measurement is sensitive to the presence of right-handed currents but also to possible scalar and tensor-type currents in the weak interaction. The aim of the second experiment is to determine the βν-correlation in β-decay by measuring the energy spectrum of the recoil ions, using a Penning trap and a retardation spectrometer. In this case the focus is on the search for scalar currents in the weak interaction. The results of the experiments presented here are complementary to results from experiments in muon decay and at high-energy colliders. This revised version was published online in July 2006 with corrections to the Cover Date.     

Intensity of muon bundles at large zenith angles and hadron interaction models at energy of 1018 eV

Characteristics of muon bundles detected with the DECOR detector are compared to predictions based on different hadron interaction models and various assumptions as to the spectrum and mass composition of primary cosmic rays. The intensity of primary cosmic rays derived from the muon bundle data is considerably higher than that measured by means of the fluorescence technique. Either changes in the hadron interaction characteristics at ultrahigh energies or a revision of the energy calibration in the fluorescence technique of measuring EAS energy is required to explain these results.     

Test of hadron interaction models in the most important energy range of secondary particles in spectra of atmospheric muons

A simple method has been proposed for testing hadron interaction models, which are used to simulate extensive air showers, in observed spectra of atmospheric muons. It has been shown that muon flux intensities in the energy range of 10²–10⁴ GeV that are calculated within the SIBYLL 2.1, QGSJETII-04, and QGSJET01 models exceed the data of the classical experiments L3 + Cosmic, MACRO, and LVD on the spectra of atmospheric muons by a factor of 1.5–2. It has been concluded that these tested models overestimate the generation of secondary particles with the highest energies in elementary events of interaction between hadrons in agreement with the LHCf and TOTEM accelerator experiments.     

μ－ CAPTURE IN NUCLEI

Using the many-body field theory the problems of μ^－ captures in nuclei are systematically studied.Without ajustable parameter,calculations are performed for the total nuclear capture rates of muon for nuclei ranging from light to heavy ones.It shows that the renormalization due to the spin-isospin-dependent strong interaction and the muon binding in the μ^－ atom are essential for a thorough understanding of this type of weak interaction processes.     

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.     

Study of condensed nitrogen by μSR method

The temperature dependences of parameters of the muon spin relaxation in liquid and crystalline nitrogen have been studied. It has been established that in condensed nitrogen there takes place a fast depolarization of muons. An anomalous behaviour of the amplitude and phase of muon precession is found in the vicinity of the orientation phase transition in solid nitrogen. It has been shown that muon spin relaxation parameters in nitrogen do not change at reduction of the oxygen impurity content from 0.7·10⁻⁴ to 10⁻⁶. The fast depolarization of muons in condensed nitrogen is apparently due to the formation of muonium atoms. To explain the phenomena observed, a model of the muonium chemical reaction is proposed. The initial phase of the muon precession has been measured as a function of the perpendicular magnetic field to determine the state of short-lived muonium in nitrogen. It has been determined that muonium in nitrogen is in an excited state. Consideration of the nuclear hyperfine interaction of muonium in condensed nitrogen makes it possible to give a qualitative explanation for the temperature dependence of the initial amplitude of the muon precession.     

On knock-on electrons of cosmic-ray muons in condensed matter (at 12° N)

The dependence of knock-on electron probability on the momenta of muons producing the knock-on electrons in condensed matter has been investigated by using a counter controlled cloud chamber. A search has also been made on the nature of the energy spectrum of the knock-on electrons from muons in the momentum region (0.80±0.05) to (1.70±0.05) Bev/c. It appears from the results of the measurements that there is a very weak dependence of knock-on electron probability on the primary muon momentum in the investigated muon spectral region (i.e. (0.80±0.05) to (1.70±0.05) Bev/c). The angular distributions and hence the energy spectra of the emergent electrons are found to be independent of muon momentum.     

Coulomb final state interaction in identical Boson interferometry

Recently, the muonic three-body systemdtμ, has aroused considerable attention in relation to the realization of a useful muon-catalyzed fusion [1, 2]. This bound system must be solved up to 6 digits in energy to establish the muon catalyzed fusion process. We applied the ATMS method [3] and the coupled-channel method [4] to the Coulomb three-body system and obtained the detailed information on the energy levels and the wave functions of the bound states. Further we investigated the effect of the nuclear interaction on the fusion rate in the bound states [5] and developed a formalism to calculate the muon sticking to⁴He [6]. In this paper we report the results obtained in our collaborations: Figure 2 shows up our main results.     

Anomalously strong relaxation of the polarization of muons in the magnetically ordered and paramagnetic states of the TbMnO<Subscript>3</Subscript> multiferroic

An anomalously strong relaxation of the muon polarization in a magnetically ordered state in the TbMnO₃ multiferroic has been revealed by the method below the μSR Néel temperature (42 K). Such a relaxation is due to the muon channel of relaxation of the polarization and the interaction of the magnetic moment of the muon with inhomogeneities of the internal magnetic field of an ordered state in the form of a cycloid. Above the Néel temperature, beginning with temperatures depending on the applied magnetic field, a two-phase state has been revealed where one phase has an anomalously strong relaxation of the muon polarization for a paramagnetic state. These features of the paramagnetic state are due to short-range magnetic order domains that appear in strongly frustrated TbMnO₃. A true paramagnetic state has been observed only at T ≥ 150 K.     

A method to limit the muon neutrino mass

Existence of a purely leptonic neutral current weak interaction may permit the use of ν_ω, e^? elastic scattering to limit the muon neutrino mass.     

Muon transverse polarization in K_{l2_\gamma } decay due to the electromagnetic final-state interaction

For the decay process K ⁺ → μ ⁺ νγ, the effect of muon transverse polarization caused by electromagnetic final-state interaction is analyzed. It is shown that, in the one-loop approximation, the muon transverse polarization varies from ?1.3×10^?3 to zero in the region of the Dalitz plot. The mean value of the muon polarization, 〈P _T〉, in the kinematical region E _γ ≥20 MeV is ?5.44×10^?4.     

On a unified theory of electromagnetism and weak interaction

A unified theory of weak and electromagnetic interaction has been developed on the basis of the assumption that the charge and mass of a lepton is of dynamical origin. According to this model, the spontaneous breakdown of symmetry generates the photon as a Goldstone boson.     

Weak neutral currents in elastic muon-nucleon scattering

Elastic polarized muon scattering is considered as an independent source of information on weak neutral currents involving muons. At low energies and high intensities cross section asymmetries are measurable which are sensitive to the right-handed weak muon charge, involve new combinations of coupling constants and depend remarkably on the details of weak nucleon form factors.     

Cosmic muon flux at shallow depths underground

The cosmic muon background has been calculated for facilities placed at shallow depths. A relatively simple formula has been proposed for the muon spectrum at sea level that ensures the calculation of the depth dependences of the vertical muon intensity and integral muon flux. Calculations show that the zenith-angle distribution of the muon flux density is almost unchanged for depths from 10 to 100 m of solid rock. The muon angular distributions are presented for all three possible cases of the arrangement of the instruments in measurements carried out on the ground and at shallow depths. It has been shown that, to eliminate the cosmic muon background, it is necessary to install an active cosmic ray shielding “umbrella” covering a zenith angle ? of no less than 80°.     

News from ASTRID

A new superferric magnetic storage ring with highly homogeneous field at 1.45 T and weak electrostatic focussing is described which has been set up at the Brookhaven National Laboratory (BNL), USA, for a precision measurement of the magnetic anomaly of the muon. The toroidal storage volume has a radius of 7 m and a diameter of 9 cm. Precision magnetic field determination based on pulsed NMR on protons in H₂O yields the field to better than 0.1 ppm everywhere within the storage region. Follow on experiments using the setup have been already suggested to search for a finite mass of the muon neutrino and to search for an electric dipole moment of the muon with significantly increased accuracy. The high homogeneity of the field suggests the usage of such devices as a mass spectrometer for heavier particles as well. This revised version was published online in July 2006 with corrections to the Cover Date.     

Exact calculation of the muon polarization function

The spin dynamics of a polarized muon at an interstitial lattice site interacting with four or six nearest neighbouring nuclear spins withJ=1/2 has been investigated. The difference from the results of the Kubo-Toyabe theory is pointed out. The interaction of a muon with four nuclei with spinJ=1 including both dipolar and quadrupolar effects is considered, and some numerical results are shown.     

Experimental study of opposite-sign dimuons produced in neutrino and antineutrino interactions

A large sample of opposite-sign dimuons, produced by the interaction of neutrinos and antineutrinos in iron, is analysed. The data agree very well with the hypothesis that the extra muon is the product of charm decay. They yield information on the strength and space-time structure of the charmproducing weak current. The strange-sea structure functionxs(x) is determined. The difference between neutrino and antineutrino dimuon production is analysed to provide a value of the Kobayashi-Maskawa weak mixing angleθ ₂.