Introduction to light scattering by Gaussian random particles

Background, current status, and future prospects are offered for “Light scattering by Gaussian random particles: Ray-optics approximation” [1]. The stochastic geometry of the random particle is called the Gaussian random sphere. The radial distance of the Gaussian sphere is lognormally distributed. Two logarithmic radial distances at a given great-circle angle apart relate to one another according to the covariance function. Sample Gaussian particles can be conveniently generated using a Legendre polynomial expansion for the covariance function and a spherical harmonics expansion for the logarithmic radial distance. The ray-optics approximation consists of the geometric-optics and forward-diffraction parts fully accounting for polarization. It is valid for particles much larger than the wavelength of incident light and with central phase differences much larger than unity. The numerical ray-tracing algorithms are general and, in principle, applicable computationally to arbitrarily shaped non-spherical particles.     

Simulation and Statistical Analysis of Random Packings of Ellipsoids

The paper describes an algorithm for the generation of random packings of ellipsoids of revolution, which is a natural generalization of an older algorithm for the case of spherical particles and belongs to the class of collective rearrangement algorithms. It yields packings with a broad spectrum of densities and geometrical properties, aspect ratio which depend on and the various parameters controlling the motions of ellipsoids during the simulation. The ellipsoid systems obtained are characterized by second‐order characteristics, namely pair correlation and orientation correlation functions. Furthermore, the constructed packings are described in a phase diagram taken from statistical physics.     

On the arithmetic of phase locking: Coupled neurons as a lattice on R2

Using methods from the geometry of numbers, we derive an explicit, global solution for the phase-locking behavior of a simple integrate-and-fire model of coupled neurons. The solution gives the ratios of phase locking (rotation numbers) attained as functions of the parameters of natural frequency and bidirectional coupling. The ordering of the ratios is related to Farey-type series and to simple continued fractions. A transition between two ratios, say $\text{a}\text{b}$ to $\text{c}\text{d}$, is possible if, and only if, ad?bc=±1. Empirically, similar ordering is evident in published data from various neuron analogues. We compare and contrast the present results with those from models based on Caianiello's equation and on more general mappings on the torus.     

Adiabatic hyperspherical approach to describing low-energy mesic-atom scattering

The adiabatic hyperspherical approach developed previously is used to describe the asymmetric mesic-atom scattering aμ+b → aμ+b, a+bμ (a, b=p, d, t) in the collision-energy range 10^?3≤?≤10² eV. Boundary conditions for J≠0 scattering states are formulated, and partial cross sections for J=0–3 are calculated. Effective numerical codes are developed, and a fast convergence of the adiabatic hyperspherical approach is demonstrated: to achieve a precision of about 1% in the calculated cross sections, it is sufficient to use a basis of not more than ten adiabatic hyperspherical functions. The results that we obtained are compared with the previous ones.     

New methods for interferometric neutron scattering lengths measurements

A skew symmetric neutron interferometer has been used for tests of a nondispersive and phase contrast variation measuring technique of scattering lengths and for the measurement of anomalous scattering lengths of strongly absorbing substances. The following bound coherent scattering lengths have been obtained: b_c(Pt)=9.60 ± 0.01 fm, b_c(Te) =5.6 ± 0.1 fm and as real parts of anomalous scattering lengths at λ=l.86Å: b_c(Sm) =0.7 ± 0.2 fm, b_c(Eu)=5.3 ± 0.3fm, b_c(Gd)=5.1 ±0.4 fm, b_c(Dy)=16.9 ± 0.3 fm.     

Interaction effects on atomic laboratory trapped Bose-Einstein condensates

We discuss the effect of inter-atoms interactions on the condensation temperature T _c of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift Δ T _c /T _c ⁰ ≈ b ₁(a/λ _{T c} ) + b ₂(a/λ _{T c} )² + ψ[a / λ _{T c} ] with a the s-wave scattering length, λ _T the thermal wavelength and ψ[a / λ _{T c} ] a non-analytic function such that ψ[0] = ψ′[0] = ψ′′[0] = 0 and |ψ′′′[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a / λ _{T c} and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b ₂ ? 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b ₂ and the empirical value of b ₂ = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.     

Model of light scattering by dust particles in the solar system: Applications to cometary comae and planetary regoliths

We analyze both the intensity and linear polarization of cosmic dust particles by using the physically exact superposition T-matrix method in a fixed orientation for various aggregates of spheres and DDA for the aggregates of Gaussian random spheres. We study both the spherical geometry (in cometary comae) and cylindrical slabs (for regoliths) up to 2000 monomers with size parameters less than ∼3. It is straightforward to produce the observed linear polarization in both geometries while the typically convex and strong opposition spike seems to require wide regolith geometries. The dependence of various parameters on light scattering has also been studied in a rather detailed form. In applications to the cometary polarization we can fit the data in six colors from UV to the J band at a very good accuracy. We, however, emphasize that we do not claim our model to be unique. The most important parameters here are the refractive index and the size distribution of submicron particles. Rest of the parameters has only a minor role. We also found that it is critically important to use several realizations from any assumed particle geometry model because corresponding scattering characteristics can vary quite a lot.     

The scattering of slow neutrons by cobalt

Different techniques have been used to determine with slow neutrons the coherent scattering amplitude b_c and the total scattering cross-section σ_sc of Co. We found values for the bound atom b_c=2.78+0.04 fm and for the free nucleus σ_sc=5.95+0.05 barns.From these quantities, the spin state scattering amplitudes b₊ and b_? corresponding to the compound nucleus states of spin I+1/2 or I?1/2 have been determined as b₊=?2.78±0.04 fm and b_?=+9.91±0.06 fm. These results are not in agreement with previous data, but they are found to be consistent with data obtained from resonance parameters.     

Cyclotron effective masses and fermi velocities for the ellipsoidal hole surfaces in molybdenum

We report on measurements of cyclotron effective masses and the dimensions k_a, k_b, and k_c for the hole ellipsoid, centered at the symmetry point N, of the Molybdenum Fermi-surface. Further, assuming parabolic band-structure, the Fermi-velocities for the holes are calculated for several crystallographic directions. The experimental measurements were performed both in a conventional reflection type experiment, and in a transmission type experiment, the latter being a new technique for observation of cyclotron resonance.     

T invariance and polarization effects in the reactions p+3He → π++4He and π++4He → p+3He

On the basis of T invariance, it is established that the dependence of the effective cross section for a binary reaction of the a+b → c+d type on the polarization vectors of primary particles a and b determines completely the polarization vectors and spin correlations for the same particles in the inverse reaction c+d → a+b induced by collisions between unpolarized primary particles c and d. By using the formalism of helicity amplitudes, polarization effects are studied in the process p+³He → π⁺+⁴He and in the inverse process π⁺+⁴He → p+³He. It is shown that, in the reaction π⁺+⁴He → p+³He, the spins of the final-state particles (proton and ³He nucleus) are strongly correlated. An expression for the correlation tensor is obtained for arbitrary values of the (p, ³He) emission angle.     

Measurement of coherent neutron scattering lengths of gases

With the neutron interferometer, measurements of the coherent neutron scattering lengths by various gases have been performed. We get the following numbers for the bound coherent scattering lengths for atoms (in fm):b _c (H) =?3.64(3),b _c (D)=6.55(8),b _c (He?3)=5.74(7),b _c (He)=3.26(3),b _c (N)=9.30(8),b _c (O)=5.83(5),b _c (Ne) =4.63(4),b _c (Ar)=2.07(2),b _c (Kr)=7.52(6),b _c (Xe)=4.69(4). In some cases greater accuracy is achieved in comparison with recommended values from the literature. The absolute values for hydrogen and deuterium measured with gaseous samples, are about 2% smaller than the values measured with liquids and other reference values.     

Thermal behavior and X-ray study of the new double salt hydrate SrCd2Cl6 · 8H2O

The double salt hydrate SrCd₂Cl₆?·?8H₂O undergoes a phase transition at T?=?318?K (phase I?–?(T?=?318)?→phase II). The structural characteristics, Raman scattering and dielectric measurements have been investigated. Phase II exhibits monoclinic symmetry (a?=?17.102(6), b?=?21.716(9), c?=?8.582(5)?Å and β?=?91.58(13)°).     

Disordered magnet near the percolation threshold

A disordered Potts magnet containing a random mixture of ferromagnetic exchange constants J_a and J_b (J_a?J_b) near the percolation threshold is considered. The scaling form for the free energy contains two crossover exponents. Duality arguments in two dimensions show that these exponents are equal. They are also shown to be equal to unity in d = 6 ? ? dimensions to order ?.     

On the applicability of a spherical basis for spheroidal layered scatterers

The applicability of an analog of the extended boundary condition method, which is popular in light-scattering theory, is studied in combination with the standard spherical basis for the solution of an electrostatic problem appearing for spheroidal layered scatterers the sizes of which are small as compared to the incident radiation wavelength. In the case of two or more layers, polarizability and other optical characteristics of particles in the far zone are shown to be undeterminable if the condition under which the appearing systems of linear equations for expansion coefficients of unknown fields are Fredholm systems solvable by the reduction method is broken. For two-layer spheroids with confocal boundaries, this condition is transformed into a simple restriction on the ratio of particle semiaxes a/b< $\sqrt 2 $ + 1. In the case of homogeneous particles, the solvability condition is that the radius of convergence of the internal-field expansion must exceed that of the expansion of an analog of the scattering field. Since homogeneous spheroids (ellipsoids) are unique particles inside which the electrostatic field is homogeneous, it is shown that the solution can be always found in this case. The obtained results make it possible to match in principle the results of theoretical and numerical determinations of the domain of applicability for the extended boundary condition method with a spherical basis for spheroidal scatterers.     

Correlations of particle orientation in monolayer films

Two-dimensional and three-dimensional models of an extended layer that consists of orientation-ally ordered particles are used to describe the ordering in monolayer films. In both models, when the distance between particles of the layer increases, the correlation function decreases to zero (for the parameter of adhesion to the substrate a = 0) or remains constant (for a ≠ 0, i.e., when the energy of interaction between the particles and the substrate is taken into account). In the latter case, this means that the layers have a long-range orientation order. The proposed models of an extended monolayer can be used to interpret data obtained by the light scattering and molecular dynamics methods for Langmuir-Blodgett films with the adhesion parameter a = 0.05 and the particle-particle interaction parameter b = 0.6 in the three-dimensional model or b = 1 in the two-dimensional model. The smaller value of b in the three-dimensional layer model can be explained by a stronger effect of cooperation of particle-particle interactions as compared to the two-dimensional layer model.     

Magnetic structure of KFeS2 — A linear chain antiferromagnet and a spin analog of active sites of two iron ferredoxins — By neutron diffraction

Magnetic structure of KFeS₂ — a spin analog of the oxidized two iron ferredoxins — was determined by the neutron diffraction method. Spins are antiferromagnetically coupled along the c-axis chain, and they make ferromagnetic sheets in the planes containing a and b axes below the transition temperature of 250.0 ± 0.5 K. The iron moment of 2.43 ± 0.03 μ_B lies in the a?c plane and is canted by 125.3 ± 0.7 degrees from a-axis at 4.2 K.     

Crystal structure of and evidence of a lattice distortion in (Me2ø2P)(TCNQ)2

(Dimethyldiphenylphosphonium)⁺(7,7,8,8-tetracyanoquinodimethanide)^?₂ is monoclinic, space group C_c, with a = 32.01(2), b = 6.56(1), $\text{c = 15.72(2)}\text{A}\text{?}$, β = 107.4(8)°. The TCNQ's stack plane-to-plane in columns parallel to b with (i) a mean interplanar spacing of 3.28 Å along the conducting chains and (ii) an exocyclic bond to quinonoid ring overlap of adjacent molecules. The conductivity along b, the needle axis, varies as $\text{σ = σ}{}_0\text{exp}\text{(}\text{?E}{}_{\mathrm{a}}\text{kT}\text{)}$ where σ_{300 K} = 0.05 S cm^?1 and E_a = 0.20 eV (Diethyldiphenylphosphonium)⁺(7,7,8,8-tetracyanoquinodimethanide)^?₂ is similarly monoclinic, space group C_c, with a = 31.48(2), b = 6.51(1), $\text{c = 15.48(2)}\text{A}\text{?}$, β = 104.2(8)°. The conductivity at 300 K and activation energy, both determined along b, are 1–10 S cm^?1 and 0.05 eV respectively. There is evidence of a lattice distortion in the dimethyl analogue only.     

Hadronic jets with a large Q⊥ lepton pair trigger

We propose to observe hadron jets in correlation with large Q⊥ transverse momentum lepton pairs. This would allow to test the theoretical idea that the large transverse momentum of the pair is mainly produced through a scattering subprocess $\text{a}\text{+}\text{b}\text{→}\text{c}\text{+γ}{}^1$. The quantum number content of these jets is a specific signature of the subprocess, especially of those involved in perturbative QCD.