Optical properties of pigmented coatings taking into account particle interactions

A T-matrix approach is used to obtain the orientation-averaged scattering and absorption cross sections of randomly oriented particle clusters, and the average angular distribution of the radiation scattered by them. The coefficients involved in the expansion of the phase function are obtained from this T-matrix approach, and used in a multiple scattering formalism to characterize the angular distribution of the diffuse radiation propagating through a particulate coating perpendicularly illuminated with collimated visible radiation. Asymmetry between forward and backward propagating diffuse radiation intensities is taken into account by means of this multiple scattering approach, which is based on solving the radiative transfer equation for successive scattering order contributions. A four-flux model is applied to compute the reflectance in terms of wavelength of the incident radiation and particle concentration. An application of the formalism is carried out to predict the optical properties of titanium dioxide pigmented polymer coatings, in terms of the pigment volume fraction and the degree of aggregation.     

Relativistic electron motion in FEL-like fields taking retarded interactions into account

Summary The interaction of two charged particles both with each other (via Lienard-Wiechert retarded potentials) and with the wiggler field of an FEL structure, along which they are launched, is computed by means of the numerical integration of the relativistic motion equations, taking also an incoming laser wave into account. The bunching effect characterizing the collective behaviour of an electron beam in FEL-like fields is simulated by assuming one of the particles to be a suitable macrocharge.     

Angular distribution of Cherenkov radiation from relativistic heavy ions taking into account deceleration in the radiator

Numerical methods are used to study the dependence of the structure and the width of the angular distribution of Vavilov-Cherenkov radiation with a fixed wavelength in the vicinity of the Cherenkov cone on the radiator parameters (thickness and refractive index), as well as on the parameters of the relativistic heavy ion beam (charge and initial energy). The deceleration of relativistic heavy ions in the radiator, which decreases the velocity of ions, modifies the condition of structural interference of the waves emitted from various segments of the trajectory; as a result, a complex distribution of Vavilov-Cherenkov radiation appears. The main quantity is the stopping power of a thin layer of the radiator (average loss of the ion energy), which is calculated by the Bethe-Bloch formula and using the SRIM code package. A simple formula is obtained to estimate the angular distribution width of Cherenkov radiation (with a fixed wavelength) from relativistic heavy ions taking into account the deceleration in the radiator. The measurement of this width can provide direct information on the charge of the ion that passes through the radiator, which extends the potentialities of Cherenkov detectors. The isotopic effect (dependence of the angular distribution of Vavilov-Cherenkov radiation on the ion mass) is also considered.     

Specific features of magnetoabsorption resulting from exactly taking into account the electronic band spectrum

Effects related to the periodicity of the carrier dispersion relation in the reciprocal space are investigated. It is shown that, under certain conditions, magnetoabsorption in crystals exhibiting such dispersion significantly differs from the magnetoabsorption in crystals characterized by a parabolic dispersion relation for charge carriers.     

Magnetic properties of doped and undoped CuO nanoparticles taking into account spin-phonon interactions

We have studied the influence of doping effects on magnetization M and Neel temperature TN of CuO nanoparticles based on the Heisenberg model including spin-phonon interactions. The experimentally obtained room temperature magnetization M is due to surface or/and doping effects in CuO nanoparticles. We have shown the importance of the effect of the spin-phonon interaction on different properties.     

Photon-electron scattering taking vacuum energy into account

We deal with photon-electron scattering between the two uncharged conducting parallel plates. The electromagnetic vacuum field between the two plates is defined by the configuration of space and also interacts with the electrons. We first deal with the relevant operators for the electron and photon fields and with the Feynman propagator. We compute theS-matrix for photon-electron scattering, taking into account the influence of the vacuum field. The computed photon-electron scattering cross section also manifests the influence of the vacuum field. We give an example for low-energy scattering of the influence of the vacuum field upon the scattering cross section.     

Electron energy spectrum in thin films,taking into account an arbitrary one-dimensional internal field

A compact and accurate solution of the specified problem is obtained in the model of an infinitely deep potential well. The solution is expressed in terms of the one-dimensional Green's function for an electron in an arbitrary field in the absence of film boundaries. The one-dimensional problem may be generalized to the three-dimensional case when the three-dimensional field allows separation of variables along and perpendicular to the plane of the film. The case of a periodic field is examined in more detail. It is shown that in the forbidden band of a bulk crystal there arise permitted film subbands.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–11, May, 1977.Thanks are due to V. L. Boneh-Bruevich for discussion of the work and for useful comments.     

A rigorous description of the energy spectrum of the isopropanol molecule taking into account the internal rotation of hydroxyl

Using the methods of a group chain, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal rotation of hydroxyl. The model is rigorous in the sense that its correctness is limited only by the correctness of a chosen symmetry of internal dynamics of the molecule.     

Fluctuations in the paraphase of improper ferroelastics taking into account indirect interactions through the field of elastic deformations

The effect of indirect interactions (through the field of elastic deformations) on the temperature dependences of a two-point correlator of the order parameter of an improper ferroelastic is studied theoretically taking into account the interaction of fluctuations at different spatial points with one another and with defective elastic fields. The latter are accounted for by using a phenomenological field of the sources of defective elastic fields. Analysis is carried out using diagrammatic expansions followed by a transition to the Dyson equation. It is proposed that the Dyson equation be approximately solved nonperturbatively using the ansatz for an exact two-point Green function of the form G_int(k)=T/[α_ij(τ)k _i k _j +β(τ)]. Such an approach makes it possible to reduce the problem to solving a system of nonlinear algebraic equations, which can effectively be solved by numerical methods. The aggregate of the assumptions made is equivalent to the mean field theory, which, however, cannot be reduced in the present case to the Ginzburg-Landau theory in view of the essentially nonlocal character of the indirect interaction via the field of elastic deformations. The results of numerical calculations are considered for a defect-free Hg₂Cl₂ crystal, for which it is shown that parameters of dispersion α_ij acquire a substantial temperature dependence in a temperature range much broader than the width of the critical region of the given crystal.     

Rigorous description of an energy spectrum of the isopropanol molecule taking into account the internal rotation of methyl tops

By using the group chain methods, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal motion of hydroxil and two identical methyl tops. The model is rigorous in the sense that its correctness is limited only by the correctness of a symmetry chosen to describe internal dynamics of the molecule.     

Solution of polarization eigenvalue problems taking depolarization into account

The shape of the transmission band of an active interferometer, a resonator with amplification and absorption cells excited by an external signal, is studied. Upon tuning the external signal frequency, the narrow saturated absorption resonances can be observed in the transmission band of the interferometer. It is shown that, by varying the gain, the resonance absorption amplitude can be compensated for one order of smallness in pressure. The effect of amplitude and frequency noises of the external signal on the results obtained is studied.     

Second-harmonic generation taking into account dispersion of nonlinear susceptibility

Second-harmonic generation in the field of an ultrashort pulse and the propagation of extremely short pulses in a medium with quadratic nonlinearity are analyzed. Second-harmonic generation is analyzed taking into account the effect of second-and third-order group velocity dispersion and dispersion of nonlinear susceptibility up to the second order. Corrections, whose order of smallness is determined by the parameter (ω_L t _p)^?1, where t _p is the pulse duration and ω_L is the carrier frequency of the pump wave, are obtained. For a large phase mismatch, two new solutions are found that describe the stationary evolution of solitary pump and second-harmonic waves in the regions of both anomalous and normal group velocity dispersions.     

Cylindrically symmetric distributions of matter taking into account pressure

A cylindrically symmetric distribution of matter under pressure which evolves with time is considered. A new class of non-steady-state solutions to the Einstein equations with cylindrical symmetry is found (for cases when the matter is under zero, constant, and time-dependent pressure). A homogeneous, anisotropic universe and an analog of the Schwarzschild solution are considered as particular cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 33–36, December, 1985.     

On the soliton spectrum of field theories with character interactions

It is shown that a soliton ansatz in field theories where the interaction is determined by the characters of compact Lie groups can be reduced to the sine-Gordon equation with higher harmonics. The mass spectrum of the basic solitons and the one-loop quantum corrections to it are found for characters of adjoint representations of compact Lie groups with nontrivial center.     

Determination of the glueball mass with allowance for the relativistic character of interaction

Nonperturbative corrections to an interaction Hamiltonian that are associated with relativistic motion and a large coupling constant are determined on the basis of an investigation of the asymptotic behavior of the polarization loop for charged scalar particles in an external gauge field. The mass spectrum of a bound state is determined analytically. The mechanism responsible for the emergence of the constituent mass of particles that form a bound state is explained. It is shown that the contribution of the vector potential and the contribution of the potential associated with a nonperturbative character of interaction cancel each other and that the slope of the Regge trajectory is determined in terms of the string tension.