Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

Cross sections for single and double ionization of atomic helium under impact by fast multiply charged ions

Expressions for the cross sections for single and double ionization of atomic helium in collisions with fast multiply charged ions are obtained in the collision parameter range υ ²≫Z≳υ, υ ₀<c, where Z and υ are, respectively, the ion charge and ion velocity, υ ₀ is the characteristic velocity of electrons in the atomic helium ground state, and c is the velocity of light. Zh. Tekh. Fiz. 68, 1–7 (March 1998)     

On transition radiation

Summary A treatment of transition radiation between two dielectric media is presented which is based on the exact expressions for the fields of the particle in the two media. Expressions for the spectral distribution of the energy emitted forward and for that emitted backward are derived. The results are in accord with experimental findings for ultra-relativistic particles. In the asymptotic region the energy spectrum becomes discrete. It is indicated how the treatment can be extended to the case of a plate and to that of a wave guide, as well as to emission by a monopole. The case of the simultaneous emission of transition radiation and Čerenkov radiation is considered and the relationship between them is clarified. In particular, it is shown that, when the particle can emit Čerenkov radiation in the forward medium, it will also emit an interference signal. This is several orders of magnitude smaller than the usual transition radiation and is concentrated in the forward direction. It is also found that the Čerenkov wave emitted by the particle in the backward medium will be partially reflected and partially refracted into the forward medium, after the particle crosses the boundary between the two media. The linear energy density for the refracted wave is calculated and it is shown that under certain feasible conditions this is amenable to experimental verification. This work was done while the author was a summer visitor at Stanford Linear Accelerator Center, Stanford University. It was supported by the U.S. Department of Energy, contract DE-AC03-76SF00515.     

Transient fields for W ions traversing Fe hosts and for Os ions traversing Fe and Ni hosts

Transient field strengths were measured for^{184, 186}W ions traversing thin, magnetized Fe foils with velocities in the range 1.8 ≲ υ/υ₀ ≲ 5.7 (υ₀ = Bohr velocity) and for^{188, 190, 192}Os ions traversing polarized Ni hosts with average velocities 〈υ/υ₀〉 ∼ 4. The present measured transient field strengths, together with previously measured results for W, Os ions, are compared with transient field strength parametrizations, and discussed in terms of microscopic models of the transient field.     

Mass shift and width broadening of ρ-mesons produced in heavy ion collisions

The mass shift Δm_ρ and width broadening ΔΓ_ρ of ρ-mesons produced in heavy ion collisions is estimated using general formulae which relate the in-medium mass shift of a particle to the real part of the forward scattering amplitude Re f(E) of this particle on constituents of the medium and ΔΓ to the corresponding cross section. It is found that the mass increases by some tens of MeV but, more importantly, the width becomes large, increasing by several hundred MeV at beam energies of a few GeV·A and by twice that amount at beam energies of about a hundred GeV·A. Received: 28 July 1998     

Novel effects of electron-phonon interaction in quasi-two-dimensional structures located in a magnetic field

This paper studies the interaction of electrons and acoustic phonons in a quasi-two-dimensional system with an asymmetric quantizing potential in a magnetic field that is parallel to the structure’s plane. It is demonstrated that the electron-phonon interaction in such a system generates an emf when there is a standing acoustic wave, as well as when the structure is heated uniformly. These phenomena are macroscopic manifestations of a universal quantum effect, which amounts to an emf being generated by any isotropic perturbation of any electron system in which the energy depends asymmetrically on the velocity υ, i.e., ε(υ)≠ε(−υ). Zh. éksp. Teor. Fiz. 115, 959–969 (March 1999)     

Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium

We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum. It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase velocity v _ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the solution of the Mathieu equation. Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998)     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

On the Motion of a Charged Particle Interacting with an Infinitely Extended System

 We study the time evolution of a charged particle moving in a medium under the action of a constant electric field E. In the framework of fully Hamiltonian models, we discuss conditions on the particle/medium interaction which are necessary for the particle to reach a finite limit velocity. We first consider the case when the charged particle is confined in an unbounded tube of ℝ³. The electric field E is directed along the symmetry axis of the tube and the particle also interacts with an infinitely many particle system. The background system initial conditions are chosen in a set which is typical for any reasonable thermodynamic (equilibrium or non-equilibrium) state. We prove that, for large E and bounded interactions between the charged particle and the background, the velocity v(t) of the charged particle does not reach a finite limit velocity, but it increases to infinite as: |v(t)−Et|≤C ₀ (1+t), where C ₀ is a constant independent of E. As a corollary we obtain that, if the initial conditions of the background system are distributed according to any Gibbs state, then the average velocity of the charged particle diverges as time goes to infinite. This result is obtained for E large enough in comparison with the mean energy of the Gibbs state. We next study the one-dimensional case, in which the estimates can be improved. We finally discuss, at an heuristic level, the existence of a finite limit velocity for unbounded interactions, and give some suggestions about the case of small electric fields. Received: 7 March 2002 / Accepted: 23 September 2002 Published online: 8 January 2003 RID="*" ID="*" Work partially supported by the GNFM-INDAM and the Italian Ministry of the University. Communicated by J.L. Lebowitz     

Fluid-dynamical representations of the Dirac equation

A relative kinetic mass operator is defined bym =c ⁻²·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force. The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H ₂ ⁺ molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors.     

On the theory of multiple scattering of sound waves by spherical particles in liquid and elastic media

Two independent systems of equations are derived for describing the scalar and vector potentials of the sound field in a liquid or elastic medium containing discrete inhomogeneities. One of the systems determines the sound field as the sum of the fields scattered by the particles according to the law of scattering by a single particle with the oscillation amplitudes governed by the properties of the inhomogeneous medium. The other system determines the sound field as the sum of the scattered fields formed in the inhomogeneous medium with the oscillation amplitudes of a particle in a homogeneous medium. Expressions relating the fields that occur in a medium consisting of N particles to the fields in a medium consisting of N − 1 particles are proposed. These expressions may simplify and diversify the methods used for computer simulation of sound fields with the aim to verify the calculations. The results of the study are valid for any particle concentrations under the condition that the scattering by a single particle is determined by its monopole, dipole, and rotary oscillations.     

Nonadiabatic corrections to the velocity of a Brownian motor with a complex potential profile

A number of laws have been established that govern the motion of a Brownian particle in a periodic potential profile for the adiabatically fast (with the time τ₀) and adiabatically slow variations in its shape. The average velocity of a particle has been calculated including a nonadiabatic contribution depending on τ₀ and the characteristic times of the system, which are determined by the characteristic features of the potential profile. It has been shown that the nonadiabatic correction to the velocity is proportional to τ₀² for a smooth potential profile and to τ₀ for a hopping movement in a potential containing barriers and wells, and this correction limits the large values of the rectification factor of motion for a high-performance motor operation mode.     

Carmeli's Cosmology Fits Data for an Accelerating and Decelerating Universe Without Dark Matter or Dark Energy

A new relation for the density parameter Ω is derived as a function of expansion velocity υ based on Carmeli's cosmology. This density function is used in the luminosity distance relation D _L. A heretofore neglected source luminosity correction factor (1 − (υ/c)²)^−1/2 is now included in D _L. These relations are used to fit type Ia supernovae (SNe Ia) data, giving consistent, well-behaved fits over a broad range of redshift 0.1 < z < 2. The best fit to the data for the local density parameter is Ω_m = 0.0401 ± 0.0199. Because Ω_m is within the baryonic budget there is no need for any dark matter to account for the SNe Ia redshift luminosity data. From this local density it is determined that the redshift where the universe expansion transitions from deceleration to acceleration is z _t = 1.095^+0.264 _−0.155. Because the fitted data covers the range of the predicted transition redshift z _t, there is no need for any dark energy to account for the expansion rate transition. We conclude that the expansion is now accelerating and that the transition from a closed to an open universe occurred about 8.54 Gyr ago.     

Flow measurement around a cycloidal propeller

Abstract  

An experimental investigation was conducted to study the flow around a cycloidal propeller. Flow fields were obtained using a particle image velocimetry system whose data acquisition was synchronized with the propeller’s angular position. The chord-based Reynolds number was Re _c = u _r c/υ = 1.4 × 10⁴, where u _r is the rotational velocity of the propeller and c is the chord length of the airfoil. Flow characteristics such as mean velocity, vorticity and the RMS value of velocity fluctuation were derived from the measurements. The results demonstrated the presence of a downwash around the propeller during the generation of lift. Detailed observations around each airfoil visualized distinct vortex shedding and reattaching flow at certain phase angles of the propeller.     

Application of PIV to over-expanded supersonic flows: Possibilities and limits

Two-dimensional velocity distributions outside a Mach 2.0 supersonic nozzle have been investigated using a digital particle im age velocimetry (PIV). Mean velocities , vor ticity field and volume dilatation field were obtained from PIV images using 0 .33 μm titanium dioxide (TiO₂) particle. The seeding particle of larger size , 1.4 μrn Ti0₂, was also used for the experimental comparison of velocity lag downstream of shock waves. The results have been compared and analyzed with schlieren photographs for the locations of shock waves and over-expanded shock structure to inspect possibilities and limits of a PIV technique to over-expanded supersonic flows. It is found that although the quantitative velocity measurement using PIV on over-expanded supersonic flows with large velocity and pressure gradients is limited, the locations of normal shock and oblique shock waves can be resolved by the axial/radial velocity fields, and over-expanded shock structure can be predicted by vorticity field and volume dilatation field which are acquired from the spatial differential of the velocity field.     

Transient-field strength measurements for52Cr traversing Fe hosts at high velocity and polarization transfer mechanisms

Transient-field strengths were measured for⁵²Cr ions traversing polarized Fe hosts at velocities up to 12υ₀ (12υ₀ =c/137 = Bohr velocity). The results are compared with predictions of various transient-field parametrizations and discussed in terms of possible mechanisms by which polarization might be transferred from the Fe host to inner vacancies of the moving Cr ions. Theg-factor of the first 2⁺ state of⁵²Cr was also measured by the transient-field technique and found to be in accord with shell model calculations.     

Detonation waves in bubble-drop media

Wave processes in chemically active multicomponent media: liquid — gas bubbles — liquid drops have been studied experimentally. Existence of detonation waves in multicomponent (bubble-drop) media has been proved. Structure of detonation waves in bubble-drop and bubble media is qualitatively identical: detonation waves are solitary waves with pulsation profile the pressure behind which is close in value to the one in unperturbed medium. Propagation velocity of detonation waves in bubble and bubble-drop media drops with the increase in medium gas phase concentration and with the decrease in carrier liquid viscosity. Presence of liquid drops decreases detonation wave velocity compared with bubble medium that does not contain liquid drops. Detonation wave propagation in multicomponent media causes gas bubbles fragmentation as well as fragmentation of individual liquid drops. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 04-03-33106).     

TDPAC characterization of tin oxides using181Ta

In connection with a general study of the evolution of tin-oxygen thin films, we report here on the hyperfine interactions of¹⁸¹Ta substitutionally replacting tin in the isolated phases SnO and SnO₂. For this purpose, pure SnO pressed powder and a thin SnO₂ film were implanted with¹⁸¹Hf. In both cases, unique quadrupole frequencies were found after thermal annealing treatments. The results indicate that the following hyperfine parameters: υ _Q = 740.6(2.1) MHz, η=0.07(2) and υ _Q = 971.5(1.9) MHz, η=0.72(1) characterize¹⁸¹Ta in SnO and SnO₂, respectively.