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.     

Form of the NH3 spectral lines in the impact approximation and analytical expressions for the relaxation parameters

The half-width and cross-relaxation parameter are calculated for a series of rotational transitions on the basis of a rigorous theory taking account of the correlational broadening of the doublet components. The absorption of the doublet lines of the transition J = 4 5 for the system NH₃-N₂ and the transition J = 5 6 for NH₃-NH₃ is analyzed. For the vibrational ground state, analytical expressions are given for the parameters and .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–7, June, 1984.     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.     

Some weak processes in electron-proton collisions

Polarization effects are investigated for processes of single production of strange particles in electron-proton collisions e^±+p ⁺+e^±. Special attention is paid to effects associated with possible application for investigation of similar processes of polarized electron beams and polarized nucleon targets. We point out the important role of the study of polarization effects for determination of the matrix element of processes of the type e^±+p ⁺+e^±.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 78–82, September, 1990.     

Notes on the classical and the nonrelativistic limits in quantum mechanics

A method is presented which can be used to discuss both the classical and also the nonrelativistic limit of quantum mechanics. A one-to-one correspondence may be established between the asymptotic convergence of the resolvent and that of the timedependent solution. In so far as the question of dynamics is concerned we investigate the relation between families of nonrelativistic Hamiltonians and the corresponding Dirac-Hamiltonians when c± or when c±0. The nonrelativistic free theory formally shows the same pattern when ±0 (the classical limit) or when ±. The investigation finally shows how the asymptotic convergence of the relativistic theory can take place under some fairly general conditions of the radiation field.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

Polarization of the secondary nucleons in thepp → ppπ 0 andpp→npπ+ reactions at 1000 MeV

The calculation of the secondary nucleons polarization in thepppp⁰ andppnp⁺ reactions at 1000 MeV is effected in the framework of the one-pion exchange model. It is shown that polarization is due to the interference of the resonant amplitude with the non-resonant amplitudes of theN virtual scattering. The angular dependence of the polarization is sensitive to the behaivour of theN scattering amplitudes off the mass shell.Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

KL,S → l+l− decays in the quark model of superconductivity type

The probabilities of K_L,S l⁺l^– decays are calculated by considering only the dominant two-lepton channel K_L,S ^{* *} l⁺l^–. The transitions K⁰ X, where X=⁰,, or (700) dominating in the K_L,S ^{* *}decay amplitudes, are described by the effective weak Lagrangian. The matrix elements of four-quark operators are calculated within the framework of the quark model of superconductivity type. It is shown that the leading contribution to matrix elements of K⁰ X transitions comes from the penguin operator matrix elements.     

Comparison of (π− d→nn withdσ(π+ d→pp) to test charge symmetry in the Δ-region

First results on ^– d are reported. The measurements were made using 8 specially designed neutron counters, which were carefully calibratedin situ. The differential cross sections atT =142, 180, 217, and 254 MeV were obtained at four angles between 0° and 90°, they are compared to ⁺ d pp data measured at the same energies and angles with the same setup. At every beam energy, the shape of the angular distributions of ^– d nn and ⁺ d pp is the same to ±2%. The absolute cross sections differ by 1 to 10%. The error in this comparison is ±4% implying a small violation of charge symmetry.Dedicated to Prof. I. laus on the occasion of his 60th birthdayDeceased     

Steady-State Spectroscopic and Fluorescence Lifetime Measurements of New Two-Photon Absorbing Fluorene Derivatives

Steady-state excitation anisotropy, lifetimes, and time-resolved emission spectra of new 2-photon absorbing fluorene derivatives were measured in aprotic solvents at room temperature. Excitation anisotropy spectra in viscous silicon oil allowed the determination of the spectral position of three electronic transitions S₀ S₁, S₀ S₂, S₀ S₃ (S_i, i = 1, 2, 3 are the singlet electronic states) and the angles ( 30°) between absorption S₀ S₁ and emission S₁ S₀ dipole moments for the first electronic transition. Solvate relaxation processes in the first excited state of the investigated fluorene molecules affect the lifetimes of these states, ₁, so that experimental values of ₁ do not correspond to those calculated by Strickler and Berg theory. The influence of the molecular concentration on the fluorescence quantum yields and ₁ have been investigated.     

Resonance interaction of antineutrinos with electrons

Expressions are given for the cross sections of the processes v_ee v and v_ee v _e ^' e' from the viewpoint of the hypothesis of weak interactions via intermediary vector mesons taking separate account of the polarizations of the electron target and the muon (electron) emission. An analysis is given of the cross sections of processes which are admissible according to both the two- and four-component theories of the neutrino. The degree of longitudinal polarization of meson emission is also determined for the interaction of incident antineutrinos (neutrinos) with a polarized target in the processes ve v, ve⁺ v⁺.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 48–53, June, 1971.The author is grateful to B. K. Kerimov for his useful advice which stimulated the appearance of this work and also to Yu. M. Kasumov for his constant assistance with the work.     

Mid-infrared light emission characteristics of Ho3+-doped chalcogenide and heavy-metal oxide glasses

Emission characteristics of Ho³⁺-doped heavy-metal oxide and chalcogenide glasses were investigated and compared with those of conventional oxide glasses. In addition to the fluorescence at approximately 1.2 m (5/6 5/8) and 2.0 m (5/7 5/8), another mid-infrared emission was observed at 2.9 m from the transition 5/6 5/7. The calculated radiative transition probability and multiphonon decay rate of the latter transition using Judd-Ofelt analysis indicated that the occurrence of the 2.9 m fluorescence was directly related to the low vibrational phonon energy of the host glasses.     

Semiclassical theory of the scattering of π-mesons by nucleons in the case of strong coupling. Part I

The scattering cross section of the reaction + N N + , + N N + is calculated by the semiclassical method. It is predicted that the latter reaction occurs through N** resonance. The mass of this resonance, the spin, and isospin are found. The zero approximation with respect to the coupling constant between the - and -mesons is considered.     

Structural Transformations in a Bi2O3 Crystal and in Bi2O3‐Based Solid Solutions in the Temperature Interval 25–750°C

The Raman scattering spectra of isostructural Bi₂O₃ and Bi_1.8Tm_0.2O₃ in the course of heating have been investigated. It is shown that the sequences of structural changes with increase in temperature differ: and ^* , respectively. In the hightemperature region, the structure takes the form of a disordered cube irrespective of the previous history of specimens.     

New approach to the old problem of muon sticking in µCF

A new approach is presented for evaluation of the muon sticking probability to helium in muon-catalyzed fusion reactions. Use of the sudden approximation is avoided. The probability _s of muon sticking to helium in the reaction dtµ µ⁴He+n, calculated with the new method, agrees with previous results. Moreover, the energy and angular distributions for the emitted muon, as well as the dependence of w_s on the energy radiated during the muon-catalyzed fusion event, have been evaluated.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

A derivation of the Broadwell equation

We consider a stochastic system of particles in a two dimensional lattice and prove that, under a suitable limit (i.e.N, 0,N²const, whereN is the number of particles and is the mesh of the lattice) the one-particle distribution function converges to a solution of the two-dimensional Broadwell equation for all times for which the solution (of this equation) exists. Propagation of chaos is also proven.Research partially supported by CNR-PS-MMAIT     

Phase Transformations α → β → γ → δ → ε in Titanium Hydride TiH x with Increase in Hydrogen Concentration

Structural phase transformations of the hcp bcc fct fcc fct ( ) type in titanium hydrides TiH _x experimentally found to occur with increase in the hydrogen concentration x are studied theoretically. Free energy phases are statistically calculated, and their concentration dependence is determined. Phase transformation temperatures are found from intersection points of free energy curves and from points of common tangents to the curves. The energy parameters of the system are estimated. The calculation results are compared with the experimental data.     

Leptonic decays of vector mesons and a possible μ+μ− resonance

The possible existence of a vector leptonic resonance (⁰) in the ^+– system is considered. We discuss the effect such a resonance would have on the g factor of the muon and also on the ratio of the partial widths of the muonic and electronic decay modes (R_V = (V ^+–)/G (V e⁺ e^–)) of the neutral vector mesons ⁰,,,, and. From the experimental values of R and R, the following values are obtained for the mass, coupling constant, and partial decay widths of the resonance: M = 872 ± 60 MeV, f²/4 = 4 ± 2) ·10^–4, ( ^{0 + –}) = 0.12±0.06 MeV, and (^{0 0 +–}) = 0.13±0.06 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 39–43, May, 1977.