Zur Chronologie des alten Ägypten

The velocityv of the propagation of discharge along the anode of a self-quenchingG—M-counter is a function of total pressureP, pressure of the quenching gasP _D, radius of the cathoder _a and of the anoder _i andV _ü the difference between working- and starting-potential. For the mixtures argon-methylal, argon-alcohol and helium-alcohol isv=v ₀·exp[k·(V _ü/V _e)^1/2] withv ₀ the velocity at the starting potentialV _e v ₀=(a+b·P _D/P)·V _n ^1/2 ·exp [(c?d·P_D/P·V _n ^?1/2 ] andV _n=V _e·(lnr _a/r _i)^?1.k, a, b, c andd are characteristical constants of the filling gas.     

Possibility of electrical conduction in filled bands

It is shown that a moving neutral particle interacting with electrons may cause an “electron drag” within a filled band. The calculation uses perturbation theory and periodic boundary conditions and is based on the one-electron model. WithN being the number and ¯v the average velocity of the electrons, one finds that for largeN the electronic velocity sumN¯v induced by the motion of the neutral particle is independent ofN, i.e. of the size of the system. The lowest-order contributions toN¯v that do not necessarily vanish are seen to be those of second order in the interaction potential. These second-order contributions are studied. In a simple one-dimensional model they are found to be, in fact, not necessarily zero and to be proportional to the velocity of the neutral particle. An order-of-magnitude formula forN¯v is derived for this case. The calculation suggests that mobile neutral particles may act as charge carriers, their effective charge possibly being much smaller than the elementary charge. In real systems, neutral particles which interact with electrons might be represented by phonons and excitons.     

Comparative study of solute trapping and Gibbs free energy changes at the phase interface during alloy solidification under local nonequilibrium conditions

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V _D , where V _D is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V _D , the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishing solute drag energy, i.e. partitionless and “dragless” solidification.     

Ein experimenteller Beitrag zu der durch langsame Primärelektronen ausgelösten Sekundärelektronenemission

The energy distribution of secondary electrons emitted from a highly degassed polycristalline Pt surface was investigated as a function of low energy (V _p ) primary electrons 5<V _p <150eV. The measurements were carried out in an UHV of better than 10^?10 mm Hg. The dependence of the numberN _S ^(Ev) of secondary electrons of a fixed energyE _v (3<E _v <12eV) on the energyV _p of the primaries (=isochromates) is studied. A lot of observations can be detected:

1. I.
   The exit depth of true secondary electrons is strongly dependent of their energy.     
   
   

Nonohmic Coulomb drag in the ballistic electron transport regime

We developed the theory of Coulomb drag current induced in a one-dimensional nanowire by the ballistic nonohmic current in a nearby parallel nanowire under the ballistic transport regime. As in the ohmic case, we predict sharp oscillations of the drag current as a function of gate voltage or chemical potential of electrons. We also study the dependence of drag current on the voltage V across the driving wire. For relatively large values of V, the drag current is proportional to V ².     

Equilibrium and stability of the charged particles’ fluxes drifting crosswise to the strong magnetic field at the expense of the Hall charge separation

The current equilibrium is investigated, where the generation of the Hall electric field on the magnetic Debye radius r _B = B ₀/(4πen _e) is considered by the drifting of the relativistic electrons crosswise to the strong magnetic field. In this case, the electron propagation is possible at the distance d that is essentially larger than the electron radius of the backward reflection in the magnetic field r ₀ ? m _e v _z c/(eB ₀). The instability of the joint drift motion of ions and electrons is investigated for the frequency oscillation w much higher than the ion cyclotron frequency w _Bi and by 4π n _i m _i c ² ? B ₀ ² and (k · B ₀) = 0. It is shown that the resonance effects by the ion beam’s plasma frequency w ? kv ₀ = w _pi leads to the generation of the nonpotential perturbations with the characteristic increment Imw ～ 10^?1 ÷ 10^{? 2} w _pi. Estimates show that the instability, associated with the propagation of the high-energy ion beam through the strong magnetic field, can essentially be like the edge-localized mode in tokamaks.     

Visualization of a Berezinskii–Kosterlitz–Thouless Topological Phase Transition in a Josephson Medium: Detection of an Anomalous Temperature Dependence of the Magnetoresistance of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7–δ</Subscript> Granular High-Temperature Superconductors

The density of states of the valence band of a p-GaAs layer formed on an n-GaAs surface owing to the bombardment by 2500-eV Ar⁺ ions has been studied by photoelectron spectroscopy. A number of peaks have been detected in the spectrum of the edge of the valence band in the binding energy range E_V < 1.2eV. Their number and energy positions correspond to the quantum confinement levels calculated for a hole quantum well on the surface with the width about the ion penetration depth R_p = 3.6nm. Electronic transitions from these levels to the bottom of the conduction band have been revealed in the spectrum of characteristic energy losses of electrons reflected from the surface. Thus, it has been shown that the action of the argon ion beam on n-GaAs results in the formation of a quantum well on the surface.     

Coulomb corrections to bremsstrahlung in the electric field of a heavy atom at high energies

We consider the differential and partially integrated cross sections for bremsstrahlung from high-energy electrons in an atomic field, with this field taken into account exactly. We use the semiclassical electron Green function and wavefunctions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed over the final-electron states are independent of screening in the leading approximation in the small parameter 1/mr _scr (r _scr is the screening radius and m is the electron mass, ? = c = 1). We also consider bremsstrahlung from a finite-size electron beam on a heavy nucleus. The Coulomb corrections to the differential probability are also very susceptible to the beam shape, while the corrections to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters mε (ε is the electron energy) and 1/mr _scr are obtained.     

Quantum Cherenkov radiation at the relative sliding of two transparent plates

Quantum Cherenkov radiation and quantum friction at the relative sliding of two transparent plates with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v _c = 2nc/(n ² + 1). The contribution from s-polarized electromagnetic waves dominates near the threshold velocity. However, in the ultrarelativistic case (v → c), contributions from both polarizations are much larger than those in a nonrelativistic theory and a new contribution from the mixing of waves with different polarizations appears. The numerical results are supplemented by analytical calculations near the threshold velocity and the speed of light.     

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ^(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z _a Z/v > 1, where Z _a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ^(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z _a and Z on κ^(p).     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Variable-range hopping conduction in LaMnO<Subscript>3 + δ</Subscript>

The temperature dependence of the electrical resistivity ρ(T) for ceramic samples of LaMnO_{3 + δ} (δ = 0.100–0.154) are studied in the temperature range T = 15–350 K, in magnetic fields of 0–10 T, and under hydrostatic pressures P of up to 11 kbar. It is shown that, above the ferromagnet-paramagnet transition temperature of LaMnO_{3 + δ}, the dependence ρ(T) of this compound obeys the Shklovskii-Efros variable-range hopping conduction: ρ(T) = ρ₀(T)exp[(T ₀/T)^1/2], where ρ₀(T) = AT ^9/2 (A is a constant). The density of localized states g(?) near the Fermi level is found to have a Coulomb gap Δ and a rigid gap γ(T). The Coulomb gap Δ assumes values of 0.43, 0.46, and 0.48 eV, and the rigid gap satisfies the relationship γ(T) ≈ γ(T _v)(T/T _v)^1/2, where T _v is the temperature of the onset of variable-range hopping conduction and γ(T _v) = 0.13, 0.16, and 0.17 eV for δ = 0.100, 0.125, and 0.154, respectively. The carrier localization lengths a = 1.7, 1.4, and 1.2 Å are determined for the same values of δ. The effect of hydrostatic pressure on the variable-range hopping conduction in LaMnO_{3 + δ} with δ = 0.154 is analyzed, and the dependences Δ(P) and γ_v(P) are obtained.     

Variations in thermal properties of diamond under isothermal compression

State equation P(V/V ₀, T) and baric dependences of thermal properties of diamond have been obtained without any fitting parameters from the interatomic pair Mie–Lennard-Jones potential and the Einstein model of a crystal. Calculations have been performed along two isotherms (at T = 300 and 3000 K) up to P = 10000 kbar = 1000 GPa, i.e., to a relative volume of V/V ₀ = 0.5. The baric dependences have been obtained for the following characteristics: isothermal elastic modulus B _T and B'(P), isochoric heat capacity C _v and C _v ' (P), isobaric heat capacity C _p ; thermal expansion coefficient α _p and α _p ' (P); and specific surface energy σ, as well as its derivatives σ'(P) and σ'(T). It is shown that for P → ∞, functions B _T (P) and σ(P) vary linearly, functions B'(P), α _p (P), C _v (P), C _p (P) and σ'(P) tend to constants, while functions α _p '(P), C _v '(P), and difference C _p (P)–C _v (P) tend to zero. Good agreement with experimental data has been demonstrated.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

A method to calculate thermal conductivity of a nonperiodic system,bamboo Si<Subscript>1−x</Subscript>Ge<Subscript>x</Subscript> nanowire with axially degraded components

For a nonperiodic system, a bamboo Si_1?x Ge _x nanowire with axially degraded components, it is impossible to obtain its phonon dispersion relations through lattice dynamic or the first principle calculation. Therefore, we present a simple and available method to solve this problem. At first, the Si_1?x Ge _x nanowire with axially degraded component is divided into several sections according to its component distribution like bamboos’ sections formed in the growth process. For each section with a given x value, we constructed a pseudo-cell to calculate its phonon dispersion relations. Thermal conductances of junctions and of each section are then calculated by the phonon mismatch model and the phonon transmission probability with diffusive and ballistic portions. The dependences of thermal conductivity on the length of each section and the gradient of degraded component between sections are presented. We studied thermal conductivity dependence on temperature, length and diameter of the Si_1?x Ge _x nanowire with axially degraded component. And we found κ ~ l ^0.8, in which the exponent 0.8 is ascribed to the competition between phonons ballistic and diffusive transport. Furthermore, thermal conductivities along axial (100), (110), and (111) directions are discussed in detail. The method provides a simple and available tool to study thermal conductivity of a non-period system, such as a quasiperiodic superlattice or a nanowire with axially degraded component.     

Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Measurement of the nuclear magnetic dipole moment of Au197 and hyperfine structure measurements in the ground states of Au197, Ag107, Ag109 and K39

Using an atomic beam magnetic resonance apparatus the nuclear magnetic dipole momentμ _I of the stable isotope Au¹⁹⁷ was measured directly with the doublet method. The result isμ _I(Au¹⁹⁷)=0.143491 (9)μ _n, uncorrected for atomic diamagnetism. Further hyperfine structure measurements were performed in the ground states of K³⁹, Ag¹⁰⁷, Ag¹⁰⁹ and Au¹⁹⁷ with the following results:Δv(K³⁹)=461.719723 (38) MHzΔv(Ag¹⁰⁷)=1712.512111 (18) MHzΔv(Ag¹⁰⁹)=1976.932075 (17) MHzΔv(Au¹⁹⁷)=6099.320184 (13) MHzg _J(Ag¹⁰⁷)/g _J(K39)=1.0000260 (20)g _J(Au¹⁹⁷)/g _J(K39)=1.0005076 (20).     

Self-consistent expansion of a multicomponent plasma into a vacuum

The problem of the one-dimensional collisionless expansion of a multicomponent plasma into a vacuum is considered. In the hydrodynamic approximation, an approximate analytical solution for an arbitrary set of ion species with masses M₁,..., M_n and charge numbers Z₁e, Z₂e,..., Z_ne is found by using the technique of self-similar variables employed by Gurevich, Pariiskaya, and Pitaevskii for the case of single-species ions. A numerical iterative algorithm is developed in which the analytical solution is used as a first approximation.     

Maslov index for power-law potentials

The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = ?V ₀/x ^s, x > 0, 0 < s < 2 The result for the potential V(x)=-V ₀/x ^1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.