Critical charge in quantum electrodynamics

The critical nuclear charge Z _cr and the critical distance R _cr in the system of two colliding heavy nuclei—they are defined as those at which the ground-state level of the electron spectrum descends to the boundary of the lower continuum, with the result that beyond them (that is, for Z>Z _cr or R<R _cr) spontaneous positron production from a vacuum becomes possible—are important parameters in the quantum electrodynamics of ultrastrong Coulomb fields. Various methods for calculating Z _cr and R _cr are considered, along with the dependence of these quantities on the screening of the Coulomb field of a nucleus by the electron shell of the atom, on an external magnetic field, on the particle mass and spin, and on some other parameters of relevance. The effective-potential method for the Dirac equation and the application of the Wentzel-Kramers-Brillouin method to the Coulomb field for Z>137 and to the two-body Salpeter equation for the quark-antiquark system are discussed. Some technical details in the procedure for calculating the critical distance R _cr in the relativistic problem of two Coulomb centers are described.     

The casimir effect as a screening effect in quantized field theory

We study the vacuum energy and the vacuum force in a system of quantized scalar fields (massive and massless) in interaction with a given screening medium. Regularization of the energy is studied and the types of determinable forces are clarified. The Casimir effect—the attraction between two conducting plates in a vacuum, and its extension to different geometries —is re-examined in this framework. Instead of the puzzling repulsion for a spherical shell conductor, an attractive force is obtained in our case. As a by-product, we obtain a potential energy between two balls of large screening power and at remote distance R, ?a₁a₂/4πR³, where a_i are the ball radii.     

Inner-shell x-ray production in adiabatic iodine -Z 2 collisions withZ 1+Z 2≧100

For heavy collision systems withZ _UA ≧100 the excitation mechanism for electrons in molecular orbitals from 2p _{1/2 1/2} up to 3d_{3/2 1/2}, which end up inK andL levels of the collision partners, is investigated for Iodine projectile velocityv between 1.3 and 3.7 a.u. (i.e. 6.3 MeV≦E _i ≦45 MeV). For 2p _{1/2 1/2} excitation a prevailing radial coupling excitation mechanism is found. In a two state approximation coupling strengths are derived for decisive isolated crossings; for the strong variation of the projectileL x-ray spectra with targetZ and impact velocity a Landau Zener type model is suggested.     

Photon propagation in a supercritical magnetic field

We show that, for the asymptotically strong (super-Schwinger) magnetic field B exceeding the critical value B_cr=m²c³/eh=4.4×10¹³G, the vacuum polarization effects become important not only in the γ-range, but also for softer electromagnetic quanta, including X-rays and optical photons, and for electromagnetic waves of radio frequencies. This is a consequence of the linearly growing term ?B/B_cr present in the vacuum polarization in an asymptotically strong magnetic field. The results may be essential in studying reflection, refraction, and splitting of X-rays, light and radio waves by magnetic fields of magnetars, and in considering emission of such waves by charged particles.     

Coulomb gauge vacua of (2+1) dimensional Yang-Mills theory

The vacuum structure of the (2+1) dimensional Yang-Mills theory is analysed. The non-trivial spherically symmetric vacuum fields in this theory can be calculated in closed form. It is shown that these non-trivial vacuum fields fall faster than 1/r at large r unlike the (3+1) dimensional case, where the vacuum is uniquely A_i = 0 if one requires lim_r→∞rA_i=0.     

Equilibrium shape and hysteresis behavior of liquid jets in transverse electric fields

The stability of a liquid jet subject to a transverse electric field is investigated in the framework of electrohydrostatic theory. It is shown that depending on the magnitude of permittivity ratio of the involved fluids S = ε_i/ε_o (inner to outer) compared to a critical permittivity ratio S_cr ≈ 27.45 the jet exhibits distinct behaviors; for S < S_cr the jet is stable and elongates indefinitely as the electric field is increased, while for S > S_cr it shows hysteresis behavior and becomes unstable beyond a critical electric capillary number Ca_cr. The results suggest that the jets are generally more stable than liquid drops.     

Structure determination in highly absorbing crystals

If electron scattering is described by a complex crystal potential

$\text{V = ∑}{}_{\mathrm{g}}\text{(v}{}_{\mathrm{g}}\text{exp}\text{(?M}{}_{\mathrm{g}}\text{+ iv}{}_{\mathrm{g}}{}^{\mathrm{i}}\text{) exp(2πiG·r)}$

,then whenever 2v_gexp(?M_g) < v₀ⁱ, it can be expected that the diffraction conditions correspond to the case of strong absorption. It is shown that in this limit a measurement of the maximum intensity of a Bragg reflection from a single crystal is equivalent to that of the total integrated intensity measured from a polycrystalline powder, for the same reflection. The absorption is sufficiently large to average the crystal wavefield over the entire range of elastic reflectivity, and an intensity measurement becomes proportional to |F|² provided that it has been maximized by small variation of the diffraction parameters about an apparent Bragg reflection to avoid the accidental excitation of strong reflections. Atomic positions however can only be determined from |F|² under certain critical assumptions concerning the role played by the atomic form factor ?(S), which are discussed. Since it is shown that in the high absorption limit maximized intensity measurements can be expected to be kinematical-like, it is also argued that there is no physical meaning to further averaging of LEED data. It may be necessary to “smooth” the data because of accidental reflections which violate the strong absorption condition.     

Divacancy contribution to impurity diffusion in noble metals

A model calculation on the contribution to electropositive impurity diffusion by divacancy processes in f.c.c. noble metals has been carried out. Four different types of divacancy configuration were considered. It is shown that ΔQ_2v = Qⁱ_2v ? Q^o_2v, the difference in the activation energy between impurity diffusi and its thermal average, ΔQ_2v^av, are generally more negative than ΔQ_tv^s as calculated by LeClaire. $\text{D}{}^{\mathrm{i}}{}_{\mathrm{2v}}\text{D}{}^{\mathrm{i}}{}_{\mathrm{1v}}$, the ratio of the impurity diffusion coefficient by the divacancy process to that by the monovacancy process, is found to be in the range of 8.2–16.7% for copper and 27.3–36.7% for silver at 1000°K, both noticeably larger than the corresponding ratio for the self-diffusion coefficients. In addition, the present calculation has shown appreciable improvement in edging closer to the experimental data than the previous calculations.     

Quantum Cherenkov radiation at the motion of a small neutral particle parallel to the surface of a transparent dielectric

Quantum Cherenkov radiation and quantum friction at the motion of a small neutral particle parallel to the surface of a transparent dielectric with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v _c = c/n. The friction force in the particle–plate configuration has been derived from the friction force in the plate–plate configuration under the assumption that one of the plates is significantly decharged. A decrease in the kinetic energy of the particle near the threshold velocity is due to its radiation and near the speed of light is determined by the heat power absorbed by the particle in the rest frame. The powers of quantum and classical Cherenkov radiation can be comparable in the relativistic case.     

Ion-electron coincidence study of the thermal He(23S) + H2 Penning reaction

A new Penning-electron-Penning-ion coincidence method is described. It is applied to the study of the thermal reaction of He(2³S) with H₂. The main results reported are separate electron energy spectra that are coincident with the three different ions formed: HeH₂⁺, HeH⁺ and H₂⁺. Based on these results it is shown that the Penning reaction of the He(2³S)/H ₂ system proceeds in two well-separated steps: (i) ionization at distances R (HeH₂) ? 6a₀ in which H₂⁺ (v) is formed in different vibrational states; and (ii) reactive collision of H₂⁺ (v) with He. For the second step the variation of the branching ratios with vibrational quantum numbers v = 0 to v = 10 is derived, and it is shown that these branching ratios may be regarded as relative vibrational-energy-dependent cross-sections for the collision of H₂⁺ (v) with He at an average relative kinetic energy of ～20 meV.     

Generation of massive neutrinos by variable fields with allowance for mixing and radiative effects

The probabilities of the processesF v _i V _j andFB v _i V _j of generation of massive neutrinos by a variable electromagnetic field, due to the contribution of four-particle peaks in the one-loop approximation with allowance for mixing, are obtained. A comparative analysis is made of the quantities considered here and of generation mechanisms discussed earlier (F v _i V _j ) in the case of vacuum neutrino synchrotron emission.Moscow State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 48–52, July, 1995.     

Quantenstatistische Thermodynamik mit mehreren Temperaturen hei nichtzerlegharer Beobachtungsebene

A set of observables describing a macroscopic system — an observation level — defines a generalized canonical statistical operator ?. The case is considered that parts þ _v of the Hamiltonian form the observation level; it leads to systems with several temperatures. Generally the Hamiltonians þ _v do not only operate in partsU _v of a product space, so that the statistical operator ? is not a product of operators ? _v . In this case the observation level is called undivisible. Examples: a system with different Zeeman and interaction temperatures; several temperatures within a system of effective spins>1/2; a Fermi or Bose gas with different spin and orbital temperatures. Zeroth, first, second, third law of such generalized statistical thermodynamics are discussed. As a consequence of the undivisibility each internal energyU _v depends on all temperaturesT ₁,...,T _v ,... Hence there are more heat capacities than in normal thermodynamics. However, there exists only one entropy for the whole system. Finally the possibility of linear transformations of the Hamiltonians þ _v , is considered.     

The A2Σ+-X2Πi electronic band system of the OD free radical: Spectroscopic data for the 0-0 sequence,and rotational term values for A2Σ+ and X2Πi

The A²Σ⁺-X²Π_i emission system of the OD radical has been recorded at high resolution from a discharge through flowing D₂O at 0.1 torr pressure. The 0-0, 1-1, and 2-2 bands of the Δv = 0 sequence have been analyzed in detail for the first time. A table of the vacuum wavenumbers and wavelengths in air of the rotational lines of these bands is presented, together with some additional measurements for the 0–1 band. The data are used to obtain a self-consistent set of term values for v′ and v″ = 0, 1, which reproduces the observed line frequencies with an average deviation of less than 0.02 cm^?1. Earlier, lower resolution data for bands with v′ and v″ = 2, 3 are also combined with the present measurements to give approximate term values for these higher levels.     

Moments of a Single Entry of Circular Orthogonal Ensembles and Weingarten Calculus

Consider a symmetric unitary random matrix V = (v _ij )_{1 ≤ i, j ≤ N} from a circular orthogonal ensemble. In this paper, we study moments of a single entry v _ij . For a diagonal entry v _ii , we give the explicit values of the moments, and for an off-diagonal entry v _ij , we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size N. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.     

FRICTIONAL BEHAVIOUR OF A BELT-DRIVEN AND PERIODICALLY EXCITED OSCILLATOR

A single-degree-of-freedom system with the parallel presence of a linear spring, a viscous damper and a contact dry friction device is studied here. The mass may slide or stick on the belt when the driver moves periodically or at a constant speed. We derive closed-form solutions according to a more complete two-phase formulation, and some interesting behaviours of the considered system are displayed. For the non-damping oscillator belt with fixed, we offer closed-form formulae for estimating the maximum displacement and the minimum driving speed amplitude needed to prevent sticking. Two friction laws are considered. For the Coulomb friction system, the positive damping term suffices to avoid the climb motion of the mass slider. We also investigate the friction behaviour of the mass slider under the influence of the friction force bound on mass speed, whose curve has negative slope when the mass speed is less than a certain value v_min. For the speed-dependent friction system we identify a critical speed denoted by v^*. According to the qualitative analysis in the phase plane we give simple criteria of the parameter values for stable equilibrium point as well as for stable limit cycle. When v varies from vv^* to v<v^*, subcritical Hopf bifurcation occurs. For the latter case the mass slider undergoes a slide-stick motion, but by increasing the driving speed the slide-stick motion can be avoided.     

The influence of tip mass offset on the stability of Beck's column

In this paper, the stability of a slender cantilever carrying a tip mass at its free end and subjected there to a follower force is investigated. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The associated boundary value problem is solved and the exact frequency equation is derived. The frequency equation is solved numerically for the case in which both the beam and the tip mass have circular cross-sections. The numerical computations indicate that the system loses stability only through flutter. The variation of the values of the critical flutter load Q_cr with the tip mass offset parameter ξ is shown graphically for four values of the tip mass density to beam density ratio p. These calculations reveal that, at sufficiently small values of ξ, Q_cr decreases sharply for increasing values of p. For values of ξ sufficiently large, however, the situation is reversed as the value of Q_cr increases with increasing p.     

Multiple-vehicle collision induced by a sudden stop in traffic flow

We study the dynamic process of the multiple-vehicle collision when a vehicle stops suddenly in a traffic flow. We apply the optimal-velocity model to the vehicular motion. If a vehicle does not decelerate successfully, it crashes into the vehicle ahead with a residual speed. The collision criterion is presented by _vi(t)/Δ_xi(t)→∞$v_i(t)/\mathrm{\Delta }{x}_i(t)\to \infty$ if Δ_xi(t)→0$\mathrm{\Delta }{x}_i(t)\to 0$ where _vi(t)$v_i(t)$ and Δ_xi(t)$\mathrm{\Delta }{x}_i(t)$ are the speed and headway of vehicle i at time t. The number of crumpled vehicles depends on the initial velocity, the sensitivity, and the initial headway. We derive the region map (or phase diagram) for the multiple-vehicle collision.     

A Class of Planar Discrete Velocity Models for Gas Mixtures

We present a method for the construction of a simple class of physically acceptable planar discrete velocity models (DVMs) for binary gas mixtures. We want five conservation laws (no more, no less) with binary collisions. We first consider a collision with a particle at rest and different possibilities for the three other particles. We associate other particles and find semisymmetric qv _i models with q=7, 9, 11, 13 and 15, symmetric with respect to the two coordinate axes, but not to an exchange between the two axes. In order to avoid spurious mass conservation relations for the species without particle at rest, we find, for the two coordinate axes, that the tips of the momenta of the particles must be on two intervals parallel to one axis with opposite values on the other. There remain some physically acceptable q=9 (the smallest) and 11, 13, 15 models (adding multiple collisions for some others). Second, we construct the associated symmetric models qv _i^qv _i, which are superpositions of the qv _i model and another ^qv _i, rotated by /2. The possible previous defect of the spurious mass invariant for qv _i is transmitted to the symmetric one. We explain another defect coming from qv _i and ^qv _i having only one common particle, then spurious invariants exist for the momentum conservations along the two axes. We get four physically acceptable symmetric 17v _i (and three intermediate semisymmetric 13v _i models) and one 25v _i model superposition of two 11v _i and two 15v _i models (other acceptable symmetric 11v _i, 13v _i, and 25v _i models exist with multiple collisions).     

Electron energy loss spectroscopy of ethylene on Ag(110) precovered with oxygen: energy dependence of the cross section

The intensities of the CH out-of-plane bending (v₇) and CH stretch (v₁) vibrations of ethylene adsorbed on Ag(l 10) precovered with oxygen have been measured in EELS as a function of beam energy from 2 to 20 eV. The energy dependence of the v₇ vibration is satisfactorily described by the dipole approximation. For the v₁ vibration, which is purely dipole forbidden, an entirely different energy dependence is found, with a maximum intensity at a beam energy of 2 eV. Comparison of the EEL intensities observed experimentally with those predicted from the dipole moments of the free molecule confirms the conclusion that the molecular plane of chemisorbed ethylene is parallel to the surface.