On the effect of the width of the scattering indicatrix on the dispersion of photon density waves in a strongly scattering medium

The dispersion of photon density waves in strongly scattering media with different widths of the scattering indicatrix is studied by the spherical harmonics method using approximations of various orders (up to the P ₇ approximation inclusive). It is shown that, beginning from the P ₃ approximation, the reduction in the velocity of photon density waves that is characteristic of the P ₁ approximation is eliminated and, independently of the width of the scattering indicatrix in the region of modulation frequencies exceeding 10¹⁰ Hz, the velocity of photon density waves asymptotically approaches the speed of light. Our study of the damping of photon density waves has shown that the formula obtained previously for the calculation of the damping coefficient (Imk(μ _s ^′ , ω)) as a function of the transport scattering coefficient and the velocity is valid at Imk ≤ μ_s (μ_s is the light scattering coefficient). The maximum growth in the damping coefficient of photon density waves with a further increase in the frequency is limited by the value of the light scattering coefficient Imk _max ≈ μ_s.     

Inner shell excitation,valence excitation and core ionization in NF3 studied by electron energy-loss and X-ray photoelectron spectroscopies

Electron energy-loss Spectroscopy (EELS) at impact energies of 2.5–3 keV has been used to obtain the electron excitation spectra for the N 1s (K-shell), F 1s (K-shell) and valence shell regions of NF₃. The inner shell spectra were recorded using small angle scattering (?1° ) while the valence shell spectrum was obtained at zero degree scattering angle. The inner shell excitation spectra show a strongly enhanced 1s→ δ^* type transition and continuum features which are typical for molecules with highly electronegative ligands. One of the peaks in an earlier published photoabsorption study of the N 1s region has been shown to be due to a N₂ impurity. The valence shell electron energy-loss spectrum shows a number of transitions which are considered to be mainly due to valence-valence type transitions, with also some evidence of Rydberg structure.The X-ray photoelectron spectra (XPS) of the N 1s and F 1s electrons along with their associated satellite structures have also been recorded using Al Kα (1486.58 eV) radiation. The vertical ionization potentials for the N 1s and F 1s electrons were found to be 414.36 (10) eV and 693.24 (10) eV, respectively. Both spectra exhibit a rich and different satellite structure. These “shake-up” features in the satellite XPS spectra are compared with continuum features of the inner shell electron energy-loss spectra and also with the valence shell spectrum.     

Virtual levels,mixed valence phase and electronic phase transitions in rare earth compounds

We discuss the influence of the Coulomb interaction between localized and conduction electrons on the properties of magnetic impurities in metals and on electronic phase transitions such as the γ—α—α' transitions in Ce and the insulator—metal transition in SmS. Due to excitonic pairing between ?-holes and s-electrons, similar to that in excitonic insulators, the virtual ?-levels in metals may acquire an extra width, which, in contrast to the width in the Anderson model, depends upon the position of the ?-level, the width being the largest when the ?-level crosses the Fermi-level. This effect stabilizes the intermediate valence phase. As a result, in the Falicov model we get either a gradual phase transition (like that found in SmTe), or a first order one, followed by the intermediate valence phase (SmS), or, which is most interesting, two successive jump-like transitions with a mixed valence in between, similar to the γ—α—α' transitions in Ce. The mixed valence phase is described here as a kind of an “excitonic insulator”. The theory also predicts the correct slopes of the phase equilibrium lines for both Ce and SmS.     

Light scattering by electrons in the excitonic absorption region of GaAs

A study has been made of the effect of the additional generation of photoexcited electrons on the excitonic absorption and luminescence spectra of ultrapure GaAs samples at T=2 K. The observed increase in the absorption coefficient for the ground (n=1) excitonic state is shown to originate from the polariton character of the energy spectrum of this state and to be due to an increase of polariton damping. The increased damping observed under electron generation is caused by polariton scattering from hot electrons as the latter undergo thermalization. As a result, the polaritons are heated. The changes observed in the luminescence spectra are produced by the reverse effect of electron heating and polariton cooling. Fiz. Tverd. Tela (St. Petersburg) 39, 1011–1016 (1997)     

A new mechanism of valence change transitions

Within the framework of the s-f hybridization model for f-metals it is shown that Kondo-type s-f scattering and f-electron damping lead to a peak in the f-electron density of states ?_f(ω). This peak arises directly above the chemical potential μ despite the deep position of the initial f-electron level ?_f relative to μ. The reconstruction of ?_f(ω) depends strongly on f-level degeneracy, temperature and pressure and it can initiate continuous or discontinuous valence change transition.     

T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells

A detailed numerical analysis of exciton-exciton interactions in semiconductor quantum wells is presented. The theory is based on the dynamics-controlled truncation formalism and evaluated for the case of resonant excitation of 1s-heavy-hole excitons. It is formulated in terms of standard concepts of scattering theory, such as the forward-scattering amplitude (or T-matrix). The numerical diagonalization of the exciton-exciton interaction matrix in the 1s-approximation yields the excitonic T-matrix. We discuss the role of the direct and exchange interaction in the effective two-exciton Hamiltonian, which determines the T-matrix, evaluated within the 1s-subspace, and also analyze the effects of the excitonic wave function overlap matrix. Inclusion of the latter is shown to effectively prevent the 1s-approximation from making the Hamiltonian non-hermitian, but a critical discussion shows that other artefacts may be avoided by not including the overlap matrix. We also present a detailed analysis of the correspondence between the excitonic T-matrix in the 1s-approximation and the well-known T-matrix governing two-particle interactions in two dimensional systems via short-range potentials. Received 3 August 2001 and Received in final form 26 December 2001     

Theory of the froissaron exchange

The results of the multi-pomeron exchange theory considered earlier, are shown to depend crucially on the threshold behaviour of the pomeron contribution at t = 4μ_π², under the condition α(0) ? 1 = Δ > α′(0) 4μ_π². The t-channel partial wave f(t) of the multi-pomeron exchange is calculated. In the limit ξ · Δ > 1, where ξ = ln s/4μ², it corresponds to the scattering on a black disk of expanding radius b₀ ≈ a · ξ where a = s/2μ_π ? α′2μ_π. Due to the threshold singularity influence, it does not violate the t-channel unitarity condition. At a sufficiently small value of the froissaron coupling constant g₀₀ ～ Δ³/a², the theory is shown to be simultaneously s-unitary.     

On the zero points of the mandelstam denominators in the complexs-plane: The general two-body process

The relativistic two-body into two-body processes are considered. The areas are described where the denominators of the Mandelstam representation vanish in the complexs-plane if the momentum transfer squaredt and the scattering angle? in the direct channel have physical values. The equations of the lines are given along which either cos?=const andt varies ort=const and cos? varies. The cuts along later lines are suggested if the continua in the crossed channels are replaced by particles. In the general mass case, it is shown that the location of the branch points in the integrand of the partial wave amplitude in the complexs-plane depends on the integration involved. However, any elastic process represents a degeneration when the mentioned dependence does not appear.     

Dynamic light scattering at the ice water interface during freezing

The 488 nm radiation of an argon laser is scattered quasi-elastically at the [0001]-face (basal plane) of a growing ice crystal. The scattering plane is the basal plane. The Rayleigh-linewidth is proportional to the square of the scattering vector. One measures about 2 krad/s at a scattering angle of 90°. The linewidth does not depend on the growth rate. Scattering is only observed once a critical growth rate ν_crit = 1,5 μ m?s has been exceeded. Then the scattering intensity depends linearly on the growth rate in the range between 0,03 μ m?s and 2,5 μ m?s. Once the surface is molten scattering vanishes and does not reappear until the growth rate has again exceeded the threshold ν_crit. The coherence properties of the scattered light indicate that the thickness of the scattering layer is less than 6 μ m. The observations are interpreted in terms of a fluctuating interface. The decay time of the fluctuations has been calculated. Satisfactory agreement with the observed Rayleigh linewidth is obtained.     

On the behavior of the πN partial wave amplitudes ats=0

The behavior of theπN partial wave amplitudes in the limitss→+0 ands→? 0 is related to backward scattering in thes- andt-channel, respectively. Assuming Mandelstam analyticity we prove with the aid of the Phragmen-Lindelöf theorem that the amplitudes for high energy backward scattering inπN→πN andππ→N¯N are equal and therefore dominated by the same exchange mechanism, namely Reggeized Fermion exchange. The dominating Regge trajectory is the Δ_δ-trajectory, and it is shown that theπN partial wave amplitudes diverge fors→±0 as \(s^{ - \alpha \Delta _\delta (0) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . — Reduced amplitudes are defined which are regular ats=0. — Using recent results ofπN backward scattering real and imaginary part of thes-wave amplitudef ₀₊ ^(?) are calculated in the interval 0≦s≦7.     

The effect of transition probability on the shape of X-ray photoelectron spectra of diamond and silicon

X-ray photoelectron spectra of valence bands in diamond and silicon have been calculated. It is shown that the probability of electron excitation from s-states is higher than that from p-states. The density of the electron states in the valence band of these crystals differs markedly from the energy distribution of photoelectrons.     

Determination of the hadronic width of the ground state in pionic hydrogen

In a new high-precision experiment at the Paul Scherrer Institut (PSI), the hadronic shift (ε _1s) and width (Γ_1s) of the ground state of pionic hydrogen, which are directly connected to the pion-nucleon isospin scattering lengths, were remeasured (PSI-Experiment R-98-01 Gotta et al. 1998). The results can be confronted with recent work of effective field theories defined in the low-energy limit of quantum chromodynamics (QCD), such as, e. g., chiral perturbation theory (ChPT). In addition, Γ_1s is connected to the pion-nucleon coupling constant f _πN. A precisely known value for f _πN allows an accurate determination of the Goldberger-Treiman discrepancy, which constitutes a measure of chiral symmetry breaking. This contribution is mainly devoted to describe a method for an accurate extraction of the hadronic width from the π ^??H data.     

s-State potts model on a Cayley tree

The Potts model is shown to exhibit a phase transition of continuous order on a Cayley tree. The leading nonanalytic part of the free energy ∣L∣ ^$\text{K}$_s involves a critical exponent $\text{K}$_s going from one to infinity as the coupling goes f rom infinity to K_BP, the Bethe-Peierls critical coupling.     

Resonant inelastic X-ray scattering (RIXS) on magnetic EuCo2P2-based systems

The features of near-edge structure around the L ₃-Eu absorption edge are investigated in EuCo₂P₂, Pr_{1 ? x} Eu _x Co₂P₂ (x = 0.2, 0.4), and Nd_0.6Eu_0.4Co₂P₂ by means of resonant inelastic X-ray scattering (RIXS). Europium is shown to be in the intermediate valence state in all compounds. A comparison is made of the values of europium intermediate valence obtained by different methods employing the synchrotron radiation. The correlation between europium valence and the observed changes of magnetic ordering in the systems under investigation is discussed.     

Electrical resistivity measurements on the Cu2MnAl heusler alloy

Electrical resistivity measurements have been performed on the Cu₂MnAl Heusler alloy in the temperature range from 4.2 to 500°K. An AT⁵ functionality was found for 4.2°K ? = T ? 15°K, evidencing a Bloch-Grüneisen electron-phonon scattering mechanism. For 270°K ? T ? 500°K the resistivity may be described by the AT + BT² polynomial. The linear term is interpreted as due to the electron-phonon scattering process while the quadratic term may be ascribed to an electronic scattering due to a Spin disorder type relaxation process. The experimental results fail to provide evidences of s-d scattering of the conduction electrons.     

Neutrino exchange and asymptotic behaviour of weak interaction cross sections

It is argued that total cross sections cannot increase asymptotically as a power of energy even in the presence of massless particle exchange. Elastic νν scattering is considered as an example. The properties of s- and t-channel partial waves are analysed and it is shown that the above statement is true if the amplitude is bounded by a polynomial in s for s→∞ and t>0 and if its singularity at t=0 is dominated by two-particle exchange.     

Determination of intrinsic FMR line broadening in ferromagnetic (Fe44Co56)77Hf12N11 nanocomposite films

Ferromagnetic nanocomposite (Fe₄₄Co₅₆)₇₇Hf₁₂N₁₁ films were deposited to investigate their intrinsic damping mechanisms due to scattering of itinerant electrons, which carry the magnetic moment of the ferromagnetic transition elements. The films were produced by reactive r.f. magnetron sputtering using a 6 in. Fe₃₇Co₄₆Hf₁₇ target. They were annealed at 400 °C in a static magnetic field, in order to induce in-plane uniaxial anisotropy. Subsequently, the films can be considered as uniformly magnetised. A ferromagnetic resonance frequency (FMR) of around 2.3 GHz could be attained, which was determined by measuring the real and imaginary parts of the frequency dependent permeability up to 5 GHz. The imaginary part, which represents a typical resonance curve, was utilised to obtain its full-width at half-maximum Δf_eff (FWHM) for the total damping behaviour characterisation. Thereby, it is possible to extract the intrinsic Gilbert damping parameter α_int, which in turn can be decomposed into two additional damping terms α_sf and α_os allocated to “spin-flip” and “ordinary scattering”, respectively. This result is correlated and discussed in terms of a verified theoretic model, to identify whether damping due to spin-flip scattering and/or ordinary scattering is dominant.     

Crossing sum rules applied to inequalities on ππ S and P waves

We use the crossing conditions for the physical absorptive parts to improve rigorous constraints of the Martin type for ππ S and P waves in the unphysical region 0 ? s ? 4. In particular, (i) inequaltities for the scattering lengths in terms of the amplitudes at s = 0, (ii) inequalities relating only I = 0 and I = 2 S waves, (iii) the inequalities of Auberson, Brander, Mahoux and Martin are considered. Though some of these new inequalities seem to be very tight, they are satisfied in nearly all tested models.     

Mössbauer study of 119Sn hyperfine interactions in the KTi1−x SnxOPO4 system

The first Mössbauer study of hyperfine interactions of ¹¹⁹Sn nuclei in the complex ferroelectric oxides KTi_1?x Sn_xOPO₄ is reported. A one-to-one correspondence between the hyperfine interaction parameters and tin atom arrangement in cis and trans positions of the structure has been established. The electric-field gradient at ¹¹⁹Sn nuclei is shown to be dominated by the contribution of valence electrons in the hybridized p and d orbitals. A linear correlation between the quadrupole displacement of the spectrum components and the average Sn-O distances has been revealed. The Mössbauer line shift data were used to estimate the number of valence s electrons of Sn⁴⁺ ions occupying the cis and trans positions throughout the x range covered.