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.     
   
   

Fine and hyperfine structure of <Emphasis Type="Italic">P</Emphasis>-wave levels in muonic hydrogen

Corrections of order α ⁵ and α ⁶ are calculated for muonic hydrogen in the fine-structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and in the hyperfine structure of the 2P _1/2-and 2P _3/2-wave energy levels. The resulting values of ΔE ^fs = 8352.08 μeV, ΔẼ ^hfs(2P _1/2) = 7819.80 μeV, and ΔẼ ^hfs(2P _3/2) = 3248.03 μeV provide reliable guidelines in performing a comparison with relevant experimental data and in more precisely extracting the experimental value of the (2P–2S) Lamb shift in the muonic-hydrogen atom. Original Russian Text ? A.P. Martynenko, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 126–136.     

Charge transfer over localized states in a TlS single crystal

It is revealed that TlS single crystals exhibit a variable range hopping conduction along a normal to their natural layers at temperatures T ≤ 230 K in a dc electric field and a nonactivated hopping conduction at low temperatures in strong electric fields. Estimates are made for the density of states near the Fermi level (N _F = 2.8 × 10²⁰ eV^?1 cm^?3 and their energy spread (ΔW = 0.02 eV), the localization radius (a = 33 Å), the average jump distance in the region of activated (R _av(T) = 40 Å) and nonactivated (R _av(F) = 78 Å) hopping conduction, and also the drop in the charge carrier potential energy along the jump distance in an electric field F: eFR = 0.006 and 0.009 eV at F = 7.50 × 10³ and 1.25 × 10⁴ V/cm, respectively.     

Recombination population of excited states of the hydrogen atom in an He-H<Subscript>2</Subscript> plasma

The population of excited states of the hydrogen atom in an afterglow plasma produced by a pulsed discharge in helium (40 Torr) with a small admixture of hydrogen ([H₂] ≈ 10¹² cm^?3) has been studied spectroscopically. The contribution from electron-ion recombination Γ ₃ ^rec to the production rate of atoms H(n = 3) has been separated. On the basis of an experiment in which the response of the spectral line intensities to the perturbation of the electron temperature in the afterglow phase was observed, the dependence Γ ₃ ^rec (T _e ～ T _e ^?(0.9–1.0) has been obtained in the region kT _e = 0.026–0.064 eV.     

Tunneling radiative recombination in <Emphasis Type="Italic">p-n</Emphasis> heterostructures based on gallium nitride and other A<Superscript>III</Superscript>B<Superscript>V</Superscript> semiconductor compounds

We present summarized data on the tunneling emission in p-n heterostructures based on GaN and on a series of cubic A^IIIB^V semiconductors, including GaAs, InP, GaSb, and (Ga, In)Sb. The emission in p-n heterostructures of the InGaN/AlGaN/GaN type in a spectral interval from 1.9 to 2.7 eV predominates at small currents (J<0.2 mA). The position of maximum ?ω_max in the spectrum approximately corresponds to the applied potential difference U:?ω_max=eU. The tunneling emission is related to a high electric field strength in GaN-based heterostructures. The radiative recombination probability is higher in the structures with piezoelectric fields. The observed spectra are compared to the spectra of tunneling emission from light-emitting diodes based on GaAs, InP, and GaSb. The experimental results for various semiconductors emitting in a broad energy range (0.5–2.7 eV) are described by the equation ?ω_max=eU=0.5–2.7 eV.     

CeAlO<Subscript>3</Subscript> crystals: Preparation and study of their electrical and optical characteristics

Crystals of cerium aluminate with perovskite structure were obtained using the cold-crucible technique. The electrical and optical properties of cerium aluminate were studied in air in the range 300–1300 K. The main characteristics of CeAlO₃ at T=300 K are a follows: electrical conductivity σ=10^?7 S/cm, dielectric permittivity ?=3000–10000 (both measured at a frequency of 1000 Hz), thermal band-gap width ΔE=2.3±0.5 eV, and optical width δE=2.65±0.25 eV, which decreases at a rate of ?0.62×10^?3 eV/K with increasing temperature in the 300-to 1500-K interval.     

Multistage radiation-stimulated changes in the microhardness of silicon single crystals exposed to low-intensity β irradiation

Radiation-stimulated and postradiation changes in the microhardness of silicon single crystals exposed to irradiation with a low-intensity flux of β particles (I = 9 × 10⁵ cm^?2 s^?1, W = 0.20 + 0.93 MeV) are studied. It is established that the inversion of the radiation-induced plastic effect occurs at a characteristic irradiation time τ_c = 75 min; i.e., irradiation of silicon single crystals for a time τ < τ_c leads to nonmonotonic reversible hardening, whereas nonmonotonic reversible softening is observed under irradiation for a time τ > τ_c. It is demonstrated that there exists a correlation between the nonmonotonic dependences of the microhardness and the concentration of electrically active defects at acceptor levels with energies E _c ? 0.11 eV, E _c ? 0.13 eV, and E _c ? 0.18 eV on the irradiation time.     

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.     

DD reaction enhancement and X-ray generation in a high-current pulsed glow discharge in deuterium with titanium cathode at 0.8–2.45 kV

The DD reaction yield (3-MeV protons) and the soft X-ray emission from a titanium (Ti) cathode surface in a periodic pulsed glow discharge in deuterium were studied at a discharge voltage of 0.8–2.45 kV and a discharge current density of 300–600 mA/cm². The electron screening potential U_e = 610 ± 150 eV was estimated in the range of deuteron energies 0.8 keV < E_d < 2.45 keV from an analysis of the DD reaction yield as a function of the accelerating voltage. The obtained data show evidence for a significant enhancement of the DD reaction yield in Ti in comparison to both theoretical estimates (based on the extrapolation of the known DD reaction cross section for E_d ≥ 5 keV to low deuteron energies in the Bosch-Halle approximation) and the results of experiments using accelerators at the deuteron energies E_lab ≥ 2.5 keV and current densities 50–500 μ A/cm². Intense emission of soft X-ray quanta (10¹³–10¹⁴ s^?1 cm^?2) was observed at an average energy of 1.2–1.5 keV. The X-ray emission intensity and the DD reaction yield enhancement strongly depend on the rate of deuterium diffusion in a thin subsurface layer of Ti cathode.     

Percolation and the electron–electron interaction in an array of antidots

A square lattice of microcontacts with a period of 1 μm in a dense low-mobility two-dimensional electron gas is studied experimentally and numerically. At the variation of the gate voltage V _g , the conductivity of the array varies by five orders of magnitude in the temperature range T from 1.4 to 77 K in good agreement with the formula σ(V _g ) = (V _g ?V _g ^* (T))^β with β = 4. The saturation of σ(T) at low temperatures is absent because of the electron–electron interaction. A random-lattice model with a phenomenological potential in microcontacts reproduces the dependence σ(T, V _g ) and makes it possible to determine the fraction of microcontacts x(V _g , T) with conductances higher than σ. It is found that the dependence x(V _g ) is nonlinear and the critical exponent in the formula σ ∝ ? (x - 1/2) ^t in the range 1.3 < t(T, V _g ) < β.     

Investigation of Rare Pion Decays with the PIBETA Spectrometer

Experimental results on pion decays obtained with the PIBETA spectrometer at the Paul Scherrer Institute (PSI) are reviewed. For pion beta decay π⁺ → π⁰е⁺ν (πβ), a precision measurement of relative probability yields Г(πβ) = [1.036 ± 0.004(stat) ± 0.004(syst) ± 0.003(π⁺→е⁺ν)] × 10^–8, which implies V_ud = 0.9728(30) for the corresponding element of the Cabibbo–Kobayashi–Maskawa mixing matrix. Using a sample of 65 × 10³ events, relative probability of the π⁺→е⁺νγ radiative pion decay (RPD) in the kinematic region of E_γ > 10 MeV and θ_eγ > 40° is measured as B^exp = 73.86(54) × 10^–8. A statistical analysis of measured E_e+ and E_γ distributions for this decay yield the values F_V = 0.0258(17) and F_A = 0.0117(17) for the pion weak formfactors. Assuming that F_V linearly depends on the е⁺ν invariant mass q² as F_V(q²) = F_V(0)(1 + aq²), the slope parameter is extracted as а = 0.10(6). The pion polarizability and neutral-pion lifetime are estimated as α_E = 2.78(10) × 10^–4 fm³ and τ(π⁰) = (8.5 ± 1.1) × 10^–17 s, respectively. The data for decays π⁺→ е⁺ ν and \({\mu ^ + } \to {e^ + }v\bar v\gamma \) have been collected and are being processed. The follow-up PEN experiment aims at reducing the uncertainty on the π⁺ → е⁺ ν relative probability by almost an order of magnitude (to 5 × 10^–4).     

Thermopower in the region of hopping conduction in TlNiS<Subscript>2</Subscript>

Samples of the composition TlNiS₂ in the hexagonal system with the unit cell parameters a=12.28 Å, c=19.32 Å, and ρ=6.90 g/cm³ are synthesized. The results of the investigation into the electrical and thermoelectrical properties of TlNiS₂ samples in the temperature range 80–300 K indicate that TlNiS₂ is a p-type semiconductor. It is found that, at temperatures ranging from 110 to 240 K, TlNiS₂ samples in a dc electric field possess variable-range-hopping conduction at the states localized in the vicinity of the Fermi level. The density of localized states near the Fermi level is determined to be N_F=9×10²⁰ eV^?1 cm^?3, and the scatter of the states is estimated as J≈2×10^?2 eV. In the temperature range 80–110 K, TlNiS₂ exhibits activationless hopping conduction. At low temperatures (80–240 K), the thermopower of TlNiS₂ is adequately described by the relationship α(T)=A+BT, which is characteristic of the hopping mechanism of charge transfer. In the case when the temperature increases to the temperature of the onset of intrinsic conduction with the activation energy ΔE=1.0 eV, there arise majority intrinsic charge carriers of both signs. This leads to an increase in the electrical conductivity σ and, at the same time, to a drastic decrease in the thermopower α; in this case, the thermopower is virtually independent of the temperature.     

Dynamical Characteristics of a Non-canonical Scalar-Torsion Model of Dark Energy

In this paper, we analyze the phase-space of a model of dark energy in which a non-canonical scalar field (tachyon) non-minimally coupled to torsion scalar in the framework of teleparallelism. Scalar field potential and non-minimal coupling function are chosen as V(?) = V₀?ⁿ and f(?) = ?^N, respectively. We obtain a critical point that behaves like a stable or saddle point depending on the values of N and n. Additionally we find an unstable critical line. We have shown such a behavior of critical points using numerical computations and phase-space trajectories explicitly.     

On wave and rheidity properties of the Earth’s crust

The properties of the Earth’s solid crust have been studied on the assumption that this crust has a block structure. According to the rotation model, the motion of such a medium (geomedium) follows the angular momentum conservation law and can be described in the scope of the classical elasticity theory with a symmetric stress tensor. A geomedium motion is characterized by two types of rotation waves with shortand long-range actions. The first type includes slow solitons with velocities of 0 ≤ V_sol ≤ c0, max = 1–10 cm s^–1; the second type, fast excitons with V₀ ≤ V_ex ≤ V_S–V_P. The exciton minimal velocity (V₀ = 0) depends on the energy of the collective excitation of all seismically active belt blocks proportional to the Earth’s pole vibration frequency (the Chandler vibration frequency). The exciton maximal velocity depends on the velocities of S (V_S ≈ 4 km s^–1) and/or P (V_P ≈ 8 km s^–1) seismic (acoustic) waves. According to the rotation model, a geomedium is characterized by the property physically close to the corpuscular–wave interaction between blocks that compose this medium. The possible collective wave motion of geomedium blocks can be responsible for the geomedium rheidity property, i.e., a superplastic volume flow. A superplastic motion of a quantum fluid can be the physical analog of the geomedium rheid motion.     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.     

Charge transport in PbMoO<Subscript>4</Subscript> crystals

Dc and ac electrical conductivity of lead molybdate crystals is studied in the temperature range 300–550 K. The electrical conductivity was shown to have electronic (hole) impurity character. The I–V characteristics are typical of a space charge-limited current. The carrier mobility was estimated to be 10^?5 cm² V^?1 sat T=300 K. The results of the study suggest the hopping mechanism of conduction in PbMoO₄ crystals.     

Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

Adiabatic elastic moduli in ZnSe : Mn<Superscript>2+</Superscript> and ZnSe : V<Superscript>2+</Superscript> crystals

The temperature dependences of the elastic moduli C ₄₄ (C ₁₁ ? C ₁₂)/2 and C _l = (C ₁₁ + C ₁₂ + 2C ₄₄)/2 of ZnSe : V²⁺ (impurity concentration, 6 × 10¹⁸ cm^?3) and ZnSe : Mn²⁺ (9.4 × 10²⁰ cm^?3) are measured in the temperature range 1.4–100.0 K at frequencies of 52 and 156 MHz. The temperature dependences of the adiabatic elastic moduli are derived. It is established that softening of the symmetry modules is observed only in the crystal with an impurity having orbitally degenerate states.     

Oxidation of the aniline–styrene epoxide-<Emphasis Type="Italic">p</Emphasis>-toluenesulfonic acid ternary system in polar solvents: Trends and mechanism

Investigation of the kinetics of oxygen absorption by the aniline–styrene epoxide-p-toluenesulfonic acid ternary system (TS) in an acetonitrile solution led to a simple equation for the oxidation rate: V _TS = k[aniline]⁰ ? [epoxide]⁰[acid]¹ at [aniline], [epoxide] ? [acid], k = 0.77 × 10^–3s^–1, and 343 K. The data obtained indicated that a complex of the three starting reagents formed before oxidation. In a mixed solvent containing tert-butanol, the dependence of V _TS on its composition was extremum. A scheme was suggested that explained the change in the dependence V _TS = k′[aniline]^–0.63[epoxide]^0.86[acid]¹ in the mixed solvent by the decomposition of the complex in the presence of alcohol.     

Specific features of anion transfer in HoF<Subscript>3</Subscript> crystals at high temperatures

The anionic conductivity of HoF₃ single crystals with a β-YF₃ structure (orthorhombic crystal system, space group Pnma) is investigated over a wide range of temperatures (323–1073 K). The unit cell parameters of HoF₃ crystals are as follows: a=0.6384±0.0009 nm, b=0.6844±0.0009 nm, and c=0.4356±0.0005 nm. It is revealed that the conductivity anisotropy of the HoF₃ crystals is insignificant over the entire temperature range covered. The crossover from one mechanism of ion transfer to another mechanism is observed near the critical temperature T_c≈620 K. The activation enthalpy of electrical conduction is found to be ΔH₁=0.744 eV at T<T_c and ΔH₂=0.43 eV at T>T_c. The fluorine vacancies are the most probable charge carriers in HoF₃ crystals. The fluorine ionic conductivities at temperatures of 323, 500, and 1073 K are equal to 5×10^?10, 5×10^?6, and 2×10^?3 S cm^?1, respectively.