The trapping of K and Na atoms by a clean W(110) surface trajectory calculations

The fraction of K and Na atoms initially trapped by the W(110) surface has been measured as a function of the incident energy (0.5–15 eV) and as a function of the incident angle. The trapping probability equals one at low incident energies (E_i ? 0.5 eV) and decreases with increasing energy. The measurements show an increase of trapping with increasing angle of incidence θ_i (measured from the surface normal). Simultaneously the desorption energies Q_i were determined from the temperature dependence of the measured mean residence time on the W(110) surface. We obtained for K: Q_i = 2.05 ± 0.02 eV, and for Na: Q_i = 2.60 ± 0.04 eV.The trapping phenomenon at a solid surface was approximated in a theoretical way by calculating the in-plane trajectory of a projectile scattered from a diatomic surface-molecule. The important feature which showed up was the conversion of tangential to normal momentum of the projectile, and thus the inapplicability of cube models. As a function of the angle of incidence two regimes can be distinguished: at the smaller angles the scattering is governed by simultaneous interaction of the projectile with two neighbouring surface atoms, and at the higher angles of incidence the single particle interaction contributes most to the momentum transfer.     

On the anisotropy ofδ-electrons from slow heavy-ion collisions in the emission angles ϑf andϕ f

Within the united-atom perturbation theory, we have calculated the probability for the ejection of electrons from theK andL shells of heavy target atoms as a function of both polar and azimuthal angle of the electron. By including multipole transitions up tol=2, we found that for asymmetric collision systems and high electron energies the angular distribution has a dipole shape. Fors _1/2 electrons, the dependence on the azimuthal angle varies strongly with impact parameterb, with a preference of electron ejection in the same direction as the scattered projectile for smallb, and in the opposite direction for largeb. This is in agreement with first experimental data.     

Dielectric behaviour of some amides and formamides dissolved in nonpolar solvents under static electric field

Structural and associational aspects of polar amides (j) like formamide, acetamide, N-methyl acetamide (NMA), N,N-dimethyl formamide (DMF), N,N-dimethyl acetamide (DMA) and acetanilide dissolved in the nonpolar solvent (i) benzene or 1,4-dioxan have been estimated from the measured static relative permittivity ε _0ij and high-frequency permittivity ε _∞ij at different weight fractions w _j s of polar solute at 35°C under static electric field using Debye model of polar liquid molecule. The static dipole moments μ _ss are compared with μ _j s reported from conductivity method and theoretical μ _theos to get exact μ _cal. μ _theos of the molecules are predicted from the available bond angles and bond moments where difference in electron affinity exists between two adjacent atoms of a polar group due to inductive, mesomeric and electromeric effects in them. Solute–solute molecular association for NMA in benzene and solute–solvent association for other amides are ascertained to arrive at their conformational structures.     

Azimuthal anchoring of a nematic liquid crystal on a grooved interface with anisotropic polar anchoring

Zhang Y J et al.[Zhang Y J,Zhang Z D,Zhu L Z and Xuan L 2011 Liquid Cryst.38 355] investigated the effects of finite polar anchoring on the azimuthal anchoring energy at a grooved interface,in which polar anchoring was isotropic in the local tangent plane of the surface.In this paper,we investigate the effects of both isotropic and anisotropic polar anchoring on the surface anchoring energy in the frame of Fukuda et al.’s theory.The results show that anisotropic polar anchoring strengthens the azimuthal anchoring of grooved surfaces.In the one-elastic-constant approximation(K11 = K22 = K33 = K),the surface-groove-induced azimuthal anchoring energy is entirely consistent with the result of Faetti,and it reduces to the original result of Berreman with an increase in polar anchoring.Moreover,the contribution of the surface-like elastic term to the Rapini-Papoular anchoring energy is zero.     

Lifetimes of Excited Alkalilike Atoms Colliding by Van der Waals Forces with Inert Gas Atoms in the Groundstate

The influence of Van der Waals forces on the lifetime of coherently excited hyperfine-states |F_im_Fi〉 and |F_im_Fi〉 of alkalilike atoms i by collissions with inert gas atoms j in the groundstate |F_jm_Fi〉 has been examined. To do this the timedependent Schrödinger equation has been solved on taking into account a static magnetic field, a radiation field and a Van der Waals force. Introducing an impact parameter model for the colliding atoms with small scattering angles which form a quasimolecule |μ〉 = |F_im_FiF_jm_Fi 〉 an expression for the cross section σ_μμ has been derived which determines the halfwidth Γ _μμ of the coherently excited states. On making use of the irreducible tensor representation the calculation of the cross-section has been reduced to the calculation of multipole transitions. The result has been applied e. g. to the coherently excited 3d¹⁰4p²P_3/2-states of Cu I colliding by dipole-dipole interaction with inert gas atoms He I, and Ar I in the ground state. The values agree well with data which have been derived from zero-level-crossing experiments.     

Equilibrium magnetic and orbital states of the manganites with four manganese atoms in the unit cell

The carrier energy spectrum and the total energy of various magnetic and orbital crystal-structure configurations of the manganites R _1?x A _xMnO₃ (R=La, Pr, Nd, Sm, etc.; A=Ca, Sr, Ba) with four manganese atoms in the unit cell have been calculated for the electron doping region x>0.5. The equilibrium magnetic and orbital configurations of the model are determined by minimizing the total energy of the system with respect to the angles θ _i ^s , φ_i, and θ _i ^o , which define the directions of the local manganese magnetic moments and the type of orbital mixing of the e _g electrons in the manganites. Assuming the parameters of the Heisenberg exchange interaction to be 0.018t<J _AFM<0.022t, the Hund exchange interaction to be J _H=2.5t, and the Jahn-Teller splitting to be Δ=1.5ty, the model with four manganese atoms in the unit cell predicts the experimentally observed magnetic phase alternation sequence G-C-A with increasing doping level y=1?x. For the values J _AFM<0.018t and y<0.28, this model allows the existence of a collinear phase H not observed earlier.     

On the transfer of line radiation in random magnetic fields

An analysis is made of the influence of a magnetic field of constant magnitude but with random orientations, described by the spherical coordinates θ and φ, on the polarization transfer in spectral lines. The assumption that the statistical properties of the field are determined by the one- and two-point probability densities P₁(x, θ, φ) and P₂(x₁, θ₁, φ₁; x₂, θ₂, φ₂) where x is the coordinate along the ray, implies that the variations of θ and φ can be considered as being due to a Markovian process in x. The expectation values of the Stokes parameters 〈Iγ〉, γ = 1, …4, are calculated functions of x or the optical depth τ. The formalism includes the limiting cases of infinite and zero correlation length. Assuming an artificial triplet and simple conditions, the results suggest that isotropic magnetic fields of the type considered have no influence on the polarization characteristics during the transfer.     

Focused scattering of low energy Li+ from Mo(001): Experimental and computer simulation results

The azimuthal dependence of the energy distribution of Li⁺, specularly scattered from Mo(001), has been obtained for several incident energies E_i. The energy distributions exhibit one or two peaks, which always lie below the kinematical single scattering energy and which have intensity and energy that depend upon the azimuth. Due to trajectory focusing, the intensity is strongly peaked along the [100] azimuth for E_i ? 500 eV, but at higher E_i the intensity enhancement is shifted toward the [310] azimuth. Results of computer simulation give reasonable agreement with experimental observations. Analysis of the simulated trajectories allows identification of the scattering mechanisms which contribute to each portion of the spectrum.     

Experimental and theoretical spectroscopic studies of ortho derivatives of methyl p-dimethylaminobenzoate

Steady-state spectroscopic studies of two ortho (-OCH₃ and -OH) derivatives of methyl p-dimethylaminobenzoate have been performed. The absorption spectra of molecules under study are analyzed taking into consideration results of quantum chemical semiempirical calculations. The fluorescence spectra of these molecules possess in polar solvents two bands, i.e., the locally excited and intramolecular charge transfer (ICT) fluorescence band. Their intensity ratio as well as the fluorescence/phosphorescence intensity ratio determined at 77 K depends on the solvent polarity. Theoretical studies of the TICT phenomenon have been made in order to explain the dual emission of molecules under study. Calculated electric dipole moments of these molecules in the ground, S₀, and excited, S₁(LE) and S₁(ICT) states, have been compared with experimentally determined data. Theoretically determined transition energies, ΔE_i, oscillator strengths, f_i, and electric dipole moments μ_S0, μ_S1(LE) and μ_S1(ICT) of the planar donor-acceptor (D/A) conformer agree with experimental data. According to Marcus theory inner- and outer-solvatation sphere reorganization energies (λ_out, λ_in) are calculated using the determined spectroscopic properties of molecules under study.     

Coefficient of ultrasound transmission from liquid helium to aluminum in the intermediate state at <Emphasis Type="Italic">T</Emphasis> ≈ 0.1 K

The coefficient α(θ) of ultrasound transmission from liquid ⁴He to an aluminum single crystal in intermediate, superconducting, and normal states at a temperature T ≈ 0.1 K is measured as a function of the polar angle θ at the azimuthal angle φ = 0. The experimental technique is based on the measurement of the Kapitza temperature jump at the interface between two media. The dependences of the transmission coefficient for the Rayleigh modes on the sound frequency (in the range 13–194 MHz) and the magnetic field strength are determined. It is demonstrated that the integrated transmission coefficient of the aluminum single crystal in the intermediate state at an angle θ_R larger than the critical value increases with an increase in the magnetic field strength. The integrals of the transmission coefficient in magnetic fields close to the field H _c are independent of the frequency. In the vicinity of H = 0, the transmission coefficient at ν > 39 MHz increases only slightly with increasing frequency. At the lowest frequencies, the transmission coefficient increases anomalously as the frequency decreases. The experimental data are compared with the results obtained in the framework of the Andreev theory. Numerical calculations are performed and the dependences α(θ, φ) for bulk modes in the range corresponding to angles smaller than the critical value are constructed for the three principal planes of the crystal, i.e., the (001), (011), and (111) planes. The dependence α(θ) is obtained for the azimuthal angle φ = 0. The width of the Rayleigh peak is estimated.     

Relation of the 2S + 1 states per site potts model to a nonlinear spin-S ising model

The interaction energy of the Potts model with 2S + 1 states per site is of the form ∑_〈i,j〉δS_iS_j where δS_iS_j is the Kronecker delta symbol. The expansion of δS_iS_j in a finite power series in S_j and S_j is explicitly given.     

Inhomogeneous threshold director reorientation in a planar nematic flexoelectric cell with finite anchoring energy

The dependence of the threshold parameters and the period of the electric-field-induced spatially periodic reorientation of the director in a flexoelectric nematic liquid crystal (NLC) on the anchoring conditions at the surface of a planar NLC cell has been studied. The threshold electric field and the corresponding wave-number of the periodic structure of the director field have been numerically calculated for arbitrary values of the anchoring energy. In the case of strong anchoring, the corresponding analytical expressions are obtained in a single-constant approximation. A decrease in the azimuthal anchoring energy leads to an increase in the intervals of possible values of the flexoelectric parameter ν and the ratio K₂/K₁ of the Frank elastic constants. A decrease in the polar anchoring energy leads to narrowing of these intervals as compared to the case of infinitely strong anchoring at the NLC cell surface.     

The residual interaction of bound nucleons-two-nucleon matrix elements deduced from transfer experiments

Matrix elements for the effective two-nucleon interaction have been deduced from the population of multiplets near closed shells as observed in direct transfer reactions. In the evaluation, the limited purity of such multiples was taken into consideration, typically by weighting the observed fractions of the two-nucleon configurations by their spectroscopic strenghts and by using the resulting energy centroids. In a few cases, off-diagonal matrix elements are available from empirical wave funcitons. The systematic errors for particle-particle matrix elements extracted directly and those obtained from Pandya transformations were found to go in opposite directions. In some cases, this feautre of the empirical mehtod could be used to suggest upper and lower “bounds” for the extracted matrix elements. Diagonal matrix elements for the empirical residual interaction show a number of features suggestive of an underlying simplicity in the interaction of bound nucleons. Within experimental uncertainties (of about 10% for T=0 matrix elements) the monopole parts of the matrix elements are fit well with a simple A?0.75 dependence, and the data available to date do not reveal any significant monopole dependence on the quantum numbers of the interacting nucleons. The usefulness of scaling is suggested. Generally, diagonal matrix elements E_J(j₁, j₂) normalized by the extracted A-dependent monopole strength agree within expected experimental uncertainties whether derived from particle-particle or particle-hole multiples and whether extracted from the beginning or the end of a major shell. For values J≠0, the diagonal E_J(j²) matrix elements seem to follow two universal functions which depend on the semi-classical coupling angles θ₁₂, but are otherwise independent on j. For j₁≠j₂ several “typical” functions ?(θ₁₂) can be constructed which fit subsets of the data and differ in a predictable way. The general features of the bound-nucleon interaction appear consistent with those of theoretical matrix elements based on a number of short-range model forces or on calculations using the G matrix approach to deal with realistic free nucleon forces. For the latter, the available theoretical numbers for j₁=j₂ agree well with the T=1 set, but they differ quantitatively from the observed matrix elements for T=0, sometimes by many (experimental) standard deviations.     

Shear flow of a nematic liquid crystal near a charged surface

The maximum alignment angle θ_eff and the effective rotational viscosity coefficient γ _i ^eff of polar liquid crystals, such as 4-n-octyloxy-4′-cyanobiphenyl (8OCB), are investigated in the vicinity of charged bounding surfaces. The quantities θ_eff and γ ₁ ^eff are calculated in the framework of the Ericksen-Leslie theory. The results of calculations demonstrate that, for a homeotropic alignment of molecules on charged indium tin oxide surfaces, the effective rotational viscosity coefficient γ _i ^eff can increase by 7.8% as compared to the bulk rotational viscosity coefficient γ₁.     

The interaction energy of three molecules united in a nanocluster by long-range attraction forces with account for Coulomb repulsion

The interaction energy of three neutral molecules that form a nanocluster is studied. It is assumed that one molecule (M₀) has a dipole moment, while the other two (M₁ and M₂) are nonpolar. The molecule interaction energy in such a nanocluster is determined by the sum of dispersion interaction energies of each pair of molecules and the sum of inductive energies of the molecules. Analytical expressions for these energies as functions of the distance between the centers of mass of the molecules have been obtained. A method for the determination of damping functions which takes the contribution of repulsive forces into account has been developed. Analytical expressions for the molecule interaction energies for a two-molecule cluster in an external field of the third molecule have been obtained. A nanocluster consisting of a molecule of polar isomer pentene C₅H₁₀ and a nonpolar molecule of polycyclic aromatic hydrocarbon pyrene C₁₆H₁₀ in the external electrostatic field of another pyrene molecule is considered. The calculation showed that the interaction energy of the two-molecule nanocluster increases by a factor of 1.5 if this cluster is in the field of the induced dipole moment of an external pyrene molecule.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms have been calculated for relative energies below 5 · 10^?3 eV (58 °K). The time independent scattering formalism ofArthurs andDalgarno was used together with an assumed Lennard-Jones type potential with anisotropicP ₂(cos?) terms in the attractive and repulsive parts. The resulting system of coupled differential equations was solved in the distorted wave and close coupling approximations for the differential and integral cross sections for elastic and inelastic (j=0→j=2) scattering. In the integral inelastic cross section several sharp resonances were found to contribute 40% to the cross section at energies below 40 °K. The resonance peaks are attributed to orbiting or short-lived compound states since they are also observed in the elastic cross section at energies which are lower by the excitation energy of 1.5 · 10^?3 eV. Finally, the effect of varying the potential parameters on the integral inelastic cross section was studied at 50 °K and a rough formula for the cross section as a function of the parameters is obtained. The formula shows that a certain ratio of repulsive and attractive anisotropies leads to a small inelastic cross section indicating a mutual cancellation.     

The RPA nuclear continuum in16O(e,e′) reactions at low momentum transfer decay on (e,e′p) and (e,e′n) reaction channels

A theoretical investigation has been performed of¹⁶O(e, e′) and¹⁶O(e, e′x) reactions at low momentum transfer in the frame of a self-consistent HF and RPA theory with a SK3 interaction. Nuclear responses and their multipole components have been calculated in the whole energy-range for the two electron kinematicsi) ? _i =67 MeV and θ=40°,ii) ? _i =130 MeV and θ=50°. The microscopic structure of HF and RPA resonating states in the energy continuum has been inferred from the calculation. Decay properties in the reaction channels (e, e′p) and (e, e′n) have been discussed in the two cases of a semidirect and a knockout reaction process.     

Asymmetry of the angular distribution of radiation of channeled relativistic electrons in optically transparent crystals

It has been shown that optical and ultraviolet radiation from relativistic electrons at planar channeling in optically transparent crystals is characterized by an unusual dependence on the polar and azimuth angles. A fraction of radiation with the frequency ω near which the derivative of the refractive index is nonzero, n'(ω) = dn(ω)/dω ≠ 0, should be observed at an angle close to π/2 with respect to the electron beam. For normal dispersion (n'(ω) > 0), this angle is smaller than π/2, whereas for anomalous dispersion (n'(ω) < 0), it is larger than π/2 (“backward” radiation). A pronounced dependence of the radiation intensity on the azimuth angle φ, i.e., azimuthal asymmetry, appears beyond the region of normal and anomalous dispersion at a fixed polar angle θ. In particular, the ratio of radiation intensities at angles φ = 0 and π/2 at θ = π/2 reaches a maximum value of about the square of the refractive index.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms are calculated for relative energies below the excitation threshold for the N₂ (j=2) rotational state. The close coupling method is used and the coupled differential equations are solved numerically. Very sharp resonances (corresponding to a lifetime of 10^?10 sec) caused by quasistable states of the N₂He system are found in the calculated cross section, when the closed channels corresponding to the N₂ (j=2) states were included in the coupled equations. The position of the resonances is compared with the calculated energy eigenvalues of the corresponding two body potential. Furthermore the equilibrium concentration of the N₂He quasistable and orbiting states is calculated at 80 °K andp _{N 2}=1 Atm. Both concentrations are found to be 1%.