Differential model for 2D turbulence

We present a phenomenological model for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order differential equation. This equation respects the scaling properties of the original Navier-Stokes equations, and it has both the −5/3 inverse-cascade and the −3 direct-cascade spectra. In addition, our model has Raleigh-Jeans thermodynamic distributions as exact steady state solutions. We use the model to derive a relation between the direct-cascade and the inverse-cascade Kolmogorov constants, which is in good qualitative agreement with the laboratory and numerical experiments. We discuss a steady state solution where both the enstrophy and the energy cascades are present simultaneously, and we discuss it in the context of the Nastrom-Gage spectrum observed in atmospheric turbulence. We also consider the effect of the bottom friction on the cascade solutions and show that it leads to an additional decrease and finite-wavenumber cutoffs of the respective cascade spectra, which agrees with the existing experimental and numerical results. The text was submitted by the authors in English.     

Derivation of vertical muon spectra at superhigh energies from our predicted primary cosmic-ray spectrum using machine interaction parameters and Feynman scaling hypothesis

Summary The vertical differential and integral, muon spectra at super-high energies,viz. up to 10 TeV have been estimated from our predicted primary spectrum of the formN(E)dE=2.4E ^−2.7dE (cm²s sr GeV)⁻¹. The accelerator data of Johnsonet al., Elbertet al. have been used for the evaluation of fractional hadronic energy moments. By using the conventional Feynman scaling hypothesis and the meson atmospheric diffusion equation after Bugaevet al., the differential and integral muon spectra have been estimated and the results are well in accord with the experimental data of Bakeret al., Allkoferet al., Ayreet al., Aminevaet al., Menon and Ramana Murthy, and Sheldonet al. in the spectral range (0.1÷10) TeV.     

Characteristics of high energy interactions I. High energy gamma-ray spectra near the top of the atmosphere

An emulsion chamber was used to study the characteristics of high energy nuclear interactions from the production spectra ofγ-rays. The emulsion chamber, which comprised of two parts, namely the detector and the graphite producer unit, was exposed to cosmic rays for about 7 hr at an atmospheric depth of 10 g cm⁻² at Hyderabad (geomagnetic latitude 7·6°N). 720 electromagnetic cascades due toγ-rays were recorded in the detector. These cascades were classified into three groups; (a)γ-rays from nuclear interactions in the detector (b)γ-rays from nuclear interactions in the producer unit and (c)γ-rays of atmospheric origin. The energies of the cascades were determined using photometric method. The spectra ofγ-rays from groups (a) and (c) were determined and compared with similar spectra obtained at greater atmospheric depths. The spectra were found to obey a power law. The spectrum ofγ-rays of atmospheric origin was found to steepen at high energies,E _r>2200 GeV.     

Recent Result of Muon Catalyzed t–t Fusion at RIKEN-RAL

We have measured X-rays and neutrons associated with the muon catalyzed t–t fusion process at the RIKEN-RAL Muon facility. In the X-ray measurement, we observed K_α and K_β X-rays originating from the muon sticking process in muon catalyzed t–t fusion, and obtained the K_α X-ray yield and the K_β/K_α intensity ratio. An average recoil energy of the (μ⁻α) atoms in a solid T₂ medium was determined from the observed Doppler broadening width of the K_α X-ray line. The obtained t–t fusion neutron has shown an exponential time spectrum with a single component and a continuous energy spectrum with a maximum energy of 9 MeV. We have determined the t–t fusion neutron yield, the t–t fusion cycling rate and the muon sticking probability from the neutron data. The obtained maximum neutron energy is a very peculiar value from the view point of the reaction Q value (11.33 MeV) with the three-particle decay mode at the exit channel: t + t → α + n + n + Q. The obtained neutron energy distribution was analyzed by a simple model with two neutron energy components; reasonable agreement has been obtained, suggesting a strong (n–α) correlation in the exit channel of the t–t muon catalyzed fusion reaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Atmospheric gamma rays in the energy region 40–1000 GeV

A large stack of lead-emulsion sandwich detector assembly was flown over Hyderabad, India. High energy gamma rays at the float altitude were unambiguously identified from the cascades they induced, and their energies reliably determined by improved methods. From an analysis of 163 gamma rays of energy ≳ 30 GeV, it is found that the differential energy spectrum is represented by the power lawJ _r (E)= 129·4E ^{−2·62±0·12} photons m⁻² sr⁻¹sec⁻¹ GeV⁻¹ at an effective atmospheric depth of 14·3 g cm⁻²; this is the first reliable balloon measurement of atmospheric gamma rays in the energy range 40–1000 GeV. After correcting for the gamma rays radiated by the primary cosmic ray electrons, the production spectrum of gamma rays, resulting from the collisions of cosmic ray nuclei with air nuclei, at the top of the atmosphere isP _r (E, 0)=8·2 × 10⁻⁴ E^2.60±0.09 photons g⁻¹sr⁻¹sec⁻¹ GeV⁻¹. The atmospheric propagation of the electromagnetic component due to the cascade process is also derived from the gamma ray production spectrum.     

Muon diffusion in Nb−H systems

We have studied the muon diffusion in various Nb−H_X systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ⁺ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.     

Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

Identification of the SO2 cold vibronic bands in the 32 200–33 300 cm−1 region

Summary The fluorescence excitation spectrum of SO₂ in the 32 200–33 300 cm⁻¹ energy region was recorded, at very low rotational temperature, in a pulsed supersonic jet. The band centres and relative intensities of about 60 well-resolved vibronic bands were determined in this region, which extends the previously available data by 800 cm⁻¹. Single vibronic level fluorescence spectra of two neighbouring vibronic bands in theD-band region along with a few filtered excitation spectra are also presented as an example of the resolution for the listed bands. The authors of this paper have agreed to not receive the proofs for correction.     

Estimation of the Sea Level Muon Spectra at Different Zenith Angles below 10 TeV Energy

The moderate energy primary cosmic ray nucleon spectrum has been calculated from the direct measurements of Webber et al., Seo et al., and Menn et al. along with the other results surveyed by Swordy. Using these directly measured primary mass composition results all particle primary nucleon energy spectrum has been constructed using superposition model to estimate the energy spectra of muons from the decay of the cosmic ray non-prompt and prompt mesons in the atmosphere. The Z-factors have been estimated from the CERN LEBC-EHS on the Lorentz invariant cross section results on pp ^±X and pp K^±X inclusive reactions and FNAL data on ^±p ^±X reactions, and duly corrected for A--A collisions. Using these Z-factors the meson energy spectra in the atmosphere have been calculated. The sea level muon energy spectra at zenith angles 0°, 45°, 72°, and 75° have been derived from the decay of non-prompt mesons by adopting standard diffusion equation of hadronic cascades. The contribution of charmed mesons to muon spectrum has also been accounted by adapting the conventional procedure. The derived differential sea level muon energy spectra for energies 10 TeV have been found to follow the power law fits of the form N (E) const. E ^-. Our estimated muon energy spectra at zenith angles 75° have been found comparable with the global spectrograph muon flux results of MARS, DEIS, and MSU groups.     

Computational studies of vibrational spectra and molecular properties of 6-methyluracil using HF, DFT and MP2 methods

Theoretical investigations of atomic charges, conformers, frontier molecular orbitals, molecular geometries, thermodynamic properties, hyperpolarizabilities and harmonic vibrational frequencies of 6-methyluracil (6MU) have been carried out using ab initio Hartree-Fock (HF), density functional theory (DFT) and second order M?ller-Plesset (MP2) methods. All calculations were performed using the GAMESS-US program package with the basis sets 6-31G(d,p) and 6-311G(d,p). FT-IR and Raman spectra of 6MU were recorded in the regions 50–4000 cm⁻¹ and 60–4000 cm⁻¹ respectively. Optimized geometries were obtained using the global optimization procedure. The calculated structural parameters for two conformers of 6MU have been compared with experimentally observed values. The energy barrier (ΔE=ELUMO-EHOMO) between the HOMO and LUMO is predicted on the basis of theoretical calculations. The simulated TD-DFT spectrum has been compared with experimental electronic spectrum for 6MU. The calculated potential energy distribution (PED) values have been utilized to perform vibrational assignment of the infrared and Raman spectra.     

Background neutron in the endcap and barrel regions of resistive plate chamber for compact muon solenoid/large hadron collider using GEANT4

In this study the performance of double gap RPC has been tested by GEANT4 Monte Carlo simulation code. The detector response calculations taken as a function of the neutron energy in the range of 0.01 eV-1 GeV have been simulated through RPC set-up. In order to evaluate the response of detector in the LHC background environment, the neutron spectrum expected in the CMS muon endcap and barrel region were taken into account. A hit rate of about 165.5 Hz cm⁻², 34 Hz cm⁻², 33.6 Hz cm⁻², and 27.0 Hz cm⁻² due to an isotropic neutron source is calculated using GEANT4 standard electromagnetic package for a 20 × 20 cm² RPC in the ME1, ME2, ME3 and ME4, respectively. While for the same neutron source and using GEANT4 package a hit rate of about 0.42 Hz cm⁻², 0.7182 Hz cm⁻² was measured for the MB1 and MB4 stations respectively. Similar characteristics of hit rates have been observed for GEANT4 low electromagnetic package.      

Temperature dependence of the muon Knight shift in graphite measured using a μSR\times 2 method

We describe a simple method by which time differential μSR spectra are collected on two different samples simultaneously. One application is to make accurate measurements of the muon precession frequency in a sample relative to a reference. As an example we report precise measurements of the muon Knight shift on HOPG graphite with H parallel to \hat c as a function of temperature. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Estimation of Sea Level Muon Energy Spectrum at High Latitude from the Latest Primary Nucleon Spectra Near the Top of the Atmosphere

The vertical muon energy spectra at sea level have been estimated from directly measured primary cosmic-ray nucleon spectrum. The hadronic energy moments have been calculated from the CERN LEBC EHS data on the Lorentz invariant cross-section results on pp ^±X and pp K^±X inclusive reactions and are duly corrected for A–A collisions. Finally, the sea level muon energy spectra have been calculated from the decay of conventional mesons, using standard formulation. The estimated muon spectra are found to be in good agreement with the directly measured muon spectra obtained from the different experiments.     

Polyspectral analysis and optimization of the frequency-domain differential phase-shift keying

Using the mathematical tool of high-order spectra (polyspectra), we consider the synthesis of optimal variants of high-order differential phase-shift keying in the frequency domain. The proposed approach allows all possible variants of the second-order differential phase-shift keying to be reduced to phase modulation of a special form of the fourth-order spectrum (trispectrum) — triphase modulation. The optimal triphase shift keying variants which have the best spectral efficiency and outperform the known variants of the second-order differential phase-shift keying in noise immunity are devised. It is shown that the noise immunity of proposed modulation is higher than that of the first-order differential phase-shift keying in the channels with simultaneous time and frequency offsets.     

Role of inelastic scattering on nuclei in cosmic-ray muon transport through matter

Spectra of hadron showers formed by cosmic-ray muons in water are calculated for two models of inelastic muon scattering on nuclei. The shape of these spectra depends on the model, and the difference is rather significant (by a factor of ∼2) for showers with very high energies. It is demonstrated that the integral muon spectra at great depths in water, calculated for a hybrid model of muon-nucleus interaction, are also significantly distorted for E > 100 TeV in comparison with the spectra calculated for the generalized model of vector dominance. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 87–90, May, 2006.     

Probing oxygen in high Tc superconductor LaSrCuO by negative muons

A novel microscopic method of muon spin rotation for negative muon (μ⁻) attached to oxygen is applied on highT _c materials LaSrCuO. The paramagnetic shift and relaxation rate are measured as a function of Sr concentration and temperature. Analysis shows the large difference in shift and relaxation between two different sites. A large anisotropy was also observed by preliminary measurements along different crystalline axes.     

Synthesis of w-CdS quantum dots and discovery of intense sub band emission owing to longitudinal optical phonons

Cadmium sulfide (CdS) quantum dots (QDs), capped with cetyltrimethylammonium bromide (CTAB), and was synthesized as stable, aqueous, colloidal nanofluid. A series of nine intense, well-resolved emission lines between 400 and 750 nm were observed for the first time when exciting the CdS QDs nanofluid with a 355-nm high energy pulsed Nd:YAG laser radiation. The energy separation between any two successive emission lines equals to the characteristic overtone energy of 295 cm⁻¹ of the longitudinal optical phonon of CdS QDs. In addition, recording the PL spectrum by using a xenon broad band light source resulted in the observation of this characteristic overtone energy of 295 cm⁻¹. In agreement with this photoluminescence characteristic, Raman spectrum exhibited four prominent Stokes lines with Raman shift equal to and multiple of 295 cm⁻¹. Transmission electron microscopy investigation showed that the CdS QDs were spherical with hexagonal wurtzite structure and had a size in the range of 5–10 nm.     

High-energy cosmic ray muons in the Earth’s atmosphere

We present the calculations of the atmospheric muon fluxes at energies 10–10⁷ GeV based on a numerical-analytical method for solving the hadron-nucleus cascade equations. It allows the non-power-law behavior of the primary cosmic ray (PCR) spectrum, the violation of Feynman scaling, and the growth of the total inelastic cross sections for hadron-nucleus collisions with increasing energy to be taken into account. The calculations have been performed for a wide class of hadron-nucleus interaction models using directly the PCR measurements made in the ATIC-2 and GAMMA experiments and the parameterizations of the primary spectrum based on a set of experiments. We study the dependence of atmospheric muon flux characteristics on the hadronic interaction model and the influence of uncertainties in the PCR spectrum and composition on the muon flux at sea level. Comparison of the calculated muon energy spectra at sea level with the data from a large number of experiments shows that the cross sections for hadron-nucleus interactions introduce the greatest uncertainty in the energy region that does not include the knee in the primary spectrum.     

Cosmic ray air showers in the knee energy region

The cosmic ray extensive air showers in the knee energy region have been studied by the North Bengal University array. The differential size spectra at different atmospheric depths show a systematic shift of the knee towards smaller shower size with the increase in atmospheric depth. The measured values of spectral indices at below and above the knee are −2.45 ±0.03 and −2.91 ±0.05 respectively. Measurements at different atmospheric depths correspond to the same values within the error limits both for below and above the knee. The present experimental results have been compared with similar such experiments