On normalization of scattering matrices of polarized radiation

The condition of normalization of scattering matrix is derived when the polarized radiation is described by the Stokes parameters I, Q, U, V. The normalization of the matrix is based on energy conservation. It has a probabilistic meaning also. When the scattering particle is nonspherical, scattered radiation may depend not only on the angle between incident and scattered radiation but on orientation of the scattering plane also. In these cases, the known change of the Stokes parameters Q, U of the incident radiation with respect to various scattering planes influences the normalization. The derived normalization includes all elements of the first line of scattering matrix and the characteristics of polarization of the incident radiation. Dependence on this polarization is appeared because the polarization influences intensities of scattered radiation and, therefore, is included in energy conservation. The routine normalization includes the first element of the scattering matrix only. These two normalizations determine the different normalizing constants of the scattering matrix. The simple computational example of scattering by the particle that has the shape of a finite cylinder is considered. This example shows that the values of normalizing constants of the routine normalization may considerably differ from the ones of the obtained normalization. The results of the study may be useful in various investigations of radiation scattering, especially in the cases when the scattering particles are nonspherical.     

The scattering of partially polarized light by oriented atoms

A compact expression is derived for the cross section of scattering of arbitrarily polarized light by oriented atomic systems, in which the dependence on the geometric parameters and on the Stokes parameters preassigning the state of partial polarization of incident radiation is explicitly separated. It is found that the cross section of any photoprocess accompanied by photon absorption (stimulated emission) contains the sum of the products of the circular and linear dichroisms of the process by the respective Stokes parameters. The effect of the atomic orientation and of the dissipation of light energy on the polarization singularities and angular distribution of scattered light is investigated. In particular, it is demonstrated that, in the case of an open dissipation channel, the angular distribution remains dependent on the atomic orientation even in the case of zero degree of circular polarization of scattered radiation.     

Approximate solution for describing polarization characteristics of radiation in a Rayleigh scattering medium

An approximate analytical solution for the 4 × 4 Green’s matrix of the problem of polarized radiation transfer in a plane-parallel layer of an absorptive Rayleigh scattering medium is proposed. It permits one to perform fast estimates of angular distributions of the Stokes parameters that are created by an incident beam with an arbitrary polarization state at different levels in a layer when the layer thickness, absorption magnitude, and albedo of the underlying surface are varied. The developed solution is compared with data obtained by the numerical doubling method. The value of the scattering coefficient for a circularly polarized radiation is shown to be somewhat smaller than that for linearly polarized radiation.     

Scattering of partially polarized light by aligned atoms

A compact expression for the cross section of scattering of an arbitrarily polarized light by aligned atomic systems is obtained, in which the dependence on the geometric parameters and the Stokes parameters specifying the state of partial polarization of the incident radiation is represented in explicit form. The effect of atomic alignment and the processes of dissipation of the light energy on the polarization specific features and the angular distribution of the scattered light is investigated. In particular, it is shown that, if a dissipative channel is accessible, the angular distribution and the degree of linear polarization of scattered light depend on the degree of circular polarization of the incident radiation η₂. Dissipative processes also induce the circular polarization of the light scattered by aligned atoms when η₂=0.     

Theory of compton scattering of polarized photons by a particle with spin 1/2

Expressions are obtained for the effective differential scattering cross section of elliptically polarized photons by a Dirac point particle initially at rest, possessing charge and anomalous magnetic moment. The particular cases of the scattering of linearly and circularly polarized photons are discussed. The case when the incident radiation is unpolarized is discussed.In conclusion the authors sincerely thank Professor A. A. Sokolov for suggesting the topic and discussing the results.     

Coupling to the elastic channel in electron impact spectroscopy: A simple second born model and its application to excitation of the 61P1 state of mercury and to the excitation of molecules

The matrix element in the infinite channel close coupling approximation responsible for coupling to the elastic channel in electron impact inelastic encounters is investigated. The contribution from the imaginary part of the energy denominator in the elastic coupling matrix element for dipole allowed transitions is shown to yield large angle differential cross sections in good agreement with experiment. This coupling mechanism predicts that the shape of the inelastic differential cross section will be dominated by the shape of the elastic cross section in the large angle high energy limit. In fact the coupling matrix element exhibits a dependence on incident energy, k², and momentum transfer, K, of the form 1/kK² which is in agreement with the theoretical predictions of Huo and means that in the limit of high incident energy the non-first-Born elastic coupling will dominate the angular dependence of the inelastic differential cross section at large scattering angles. In the case of molecular electron impact spectra it is shown that the analog of the Massey—Moore coherence features depending on the symmetry of the states involved in the excitation process will also occur in the coupling contribution. It is suggested that this new mechanism for producing coherent features in inelastic differential cross sections may be the explanation of the coherent features observed experimentally by Karle and Swick.It can be concluded on the basis of the results obtained here that the coupling to the elastic cross section provided by the imaginary contribution from the second Born energy denominator is sufficient to explain presently available experimental data on the large angle differential cross section and spin polarization. The simple coupling model was found to be inadequate to explain the small angle differential cross section in the range 10° < θ < 30° even at incident energies as high as 400 eV. The calculations also showed significant differences between first and second Born calculations at zero scattering angle. No conclusion can be drawn about this observation as all the omitted terms should make significant contributions in the small angle region. It is important to again emphasize that the large angle scattering even in the limit of high incident electron energy will be completely dominated by the coupling to the elastic channel^{7, 11}. On the basis of this work it appears that the coherent structure in the large angle inelastic differential cross section observed by Swick and Karle^{12, 13} at incident electron energies in the keV region may well be due to coupling to the elastic channel.     

Multiple scattering of elliptically polarized light in two-dimensional medium with large inhomogeneities

For elliptically polarized light incident on a two-dimensional medium with large inhomogeneities, the Stokes parameters of scattered waves are calculated. Multiple scattering is assumed to be sharply anisotropic. The degree of polarization of scattered radiation is shown to be a nonmonotonic function of depth when the incident wave is circularly polarized or its polarization vector is not parallel to the symmetry axis of the inhomogeneities.     

Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices

We present an algorithm for polarized radiative transfer in a vertically stratified system consisting of two plane-parallel media with different refractive indices. It is based on the discrete ordinate method and includes multiple elastic scattering, thermal radiation, Fresnel reflection and transmission, incident parallel-beam or isotropic radiation at the top of the upper medium and bidirectional reflection at the bottom of the lower medium. Comparisons with results from Monte Carlo simulations show that the discrete-ordinate code provides accurate results for all four elements of the Stokes vector (I, Q, U, and V) at a speed that is orders of magnitude faster.     

Theory of compton scattering of polarized photons by a polarized particle with spin 1/2

Formulas are obtained for the differential effective scattering cross section when elliptically polarized photons are scattered by a point, initially stationary, a polarized Dirac particle possessing a charge, and an anomalous magnetic moment. The cases in which the incident radiation is unpolarized, linearly polarized, and circularly polarized are analyzed.Translated from Izvestiya VUZ. Fizika, Vol. 11, No. 8, pp. 121–128, August, 1968.In conclusion we thank Professor A. A. Sokolov for suggesting this problem.     

On the problem of polarization characteristics of radio waves in a randomly inhomogeneous magnetoactive plasma

Expressions for the Stokes parameters when radio waves propagate in a turbulent magnetoactive plasma have been obtained using a refractive scattering method. The problem of the spatial coherence of polarized radiation is considered. Expressions for the correlation functions and fluctuation dispersions of the Stokes parameters are found in the case of saturated wave field fluctuation. It is shown that the fluctuation of the circular polarized component will be observed in the received radiation even if the circular polarization is absent in the radiation that is incident on the magnetoactive plasma slab. A method is proposed to define the preference orientation of the magnetic field in the inhomogeneous layer of space plasma, which is biased on the simultaneous measurement of the space correlation functions of the I, V Stokes parameter fluctuation and Faraday rotation of the radiation polarization plane from the source with known polarization characteristics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1007–1013, August, 1996.This work was supported in part by the Russian Foundation for Fundamental Research under Project No. 96-02-18632.     

Dissociative recombination of electrons and O 2 + molecular ions in the field of intense visible laser radiation

We analyze the low-temperature dissociative recombination reaction e ^?+O ₂ ⁺ → O(¹ D)+O(³ P) in the field of visible monochromatic laser radiation. The analysis is performed in terms of the multichannel quantum defect theory using the stationary formalism of the radiative collision matrix. We calculate the dependences of the reaction cross section on the incident electron energy, the external electromagnetic field strength and frequency, and also the angle between the directions of the electron beam and the electric vector for linearly polarized radiation. The cross section is shown to increase by several orders of magnitude for a certain choice of these parameters, suggesting the possible laser stimulation of this reaction.     

Scattering of polarized photons at a free magnetic moment

Formulas are derived for the differential effective scattering cross section for elliptically polarized radiation, the magnetic moment being initially at rest with the spin oriented. The cases of linear and circular polarization are considered in detail, as is the case of unpolarlzed radiation. The formulas give the polarization of the scattered radiation as a function of the incident polarization and of the spin orientation.We are indebted to Prfessor A. A. Sokolov for proposing the topic and for discussing the results.     

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.     

Polarization resolved stimulated raman scattering: probing depolarization ratios of liquids

Polarization resolved stimulated Raman scattering (SRS) signal is described in the case of isotropic media and linearly polarized incident fields. The model gives simple expressions for the two perpendicularly polarized SRS signals I_X and I_Y, detected along the X and Y directions, respectively, as a function of the incident pump and Stokes polarization angles. We find that Raman depolarization ratio can be simply obtained from the ratio of the SRS intensities detected along the X and Y axis. These theoretical findings are supported by polarization resolved SRS measurements performed on polarized and depolarized bands of cyclohexane. Copyright © 2011 John Wiley & Sons, Ltd.     

Noneikonal approach to the scattering of hadrons from nuclei III. pd scattering at intermediate energy

A noneikonal theory, formulated originally for hadron scattering by spherically symmetric nuclei, is extended to the case of nonspherical densities. The results are applied to 600-MeV and 1-GeV proton elastic scattering by polarized and aligned deuterons. Around the diffraction minimum 0.2 ? q² ? 0.6 (GV/c)², and for large q² ? 1 (GeV/c)², our predictions for the differential cross section differ considerably from those obtained in Glauber theory. Experimental checks of our predictions are discussed.     

Ne-HF体系的相互作用势及散射截面的密耦计算

利用非线性最小二乘法拟合在CCSD(T)/aug-cc-pVQZ理论水平下计算的相互作用能,得到了基态Ne-HF体系相互作用势的解析表达式.基于拟合的CCSD(T)势,通过密耦计算得到了入射能量分别为60,75,100和150meV 时,Ne-HF散射的微分截面和分波截面,详细讨论了散射截面随能量的变化趋势以及态-态激发截面对总非弹性散射截面的影响. 关键词： 相互作用势 散射截面 密耦计算 Ne-HF体系     

均匀各向异性介质球散射的解析研究

将均匀各向异性介质重构为电学上的无耗各向同性介质,得到了重构目标的散射截面;进而得到了主坐标系中无耗各向异性介质球的散射截面,将介质退化到各向同性介质时,各向异性介质球的散射截面与Mie理论完全一致,验证了所得结果的正确性;仿真结果表明:散射截面正比于目标介电常数张量的元素且随入射方向的变化而变化;所得结果为复杂形体各向异性介质目标的散射评判提供了理论基础。     

Analyzing power fluctuations in nuclear reactions

The joint analysis of differential analyzing power (AP) and differential cross section in the nuclear reactions of +J ₁→J ₂ +J ₃ type in the region of strongly overlapping resonances are presented. Consideration is valid in the absence of the channel-channel compound nuclear correlations. The fluctuations of AP and cross section are proved to be statistically correlated, the greater the direct contribution to the reaction cross section the stronger this correlation. For the purely statistical reactions the correlation is absent. It is shown that the joint investigation of the AP and cross section fluctuations gives possibility to extract the direct reaction AP and the separate the direct and compound nucleus contributions into the reaction cross section. In particular it can be done by means of the statistical correlation (SC) analysis. Furthermore, the SC analysis may serve as a test for revealing the intermediate structure involved in the reaction. Finally, the joint study of differential AP and differential cross section may be used to determine the spins of nuclear levels and polarization of incident beam. The results are employed to separate the compound and direct contributions in the inelastic scattering of polarized protons on²⁸Si. Comparison with experiment quantitatively supports the existence of the SC between the fluctuations of AP and cross section. Possible extension of the SC analysis to the case of the presence of channel-channel compound nuclear correlations are discussed.     

Nonresonant mechanism of scattering of electromagnetic waves by sea surface: Scattering by steep sharpened waves

We develop an asymptotic theory of nonresonant backscattering of electromagnetic waves in the X-band by the ocean surface. Small-height (5÷20 cm) breaking surface waves with sharpened edges are assumed to be the main cause of nonresonant scattering. Using the methods of physical optics and geometrical theory of diffraction, we calculate the contribution of breaking sharpened waves to the scattering cross section for two orthogonal polarizations of electromagnetic scattering. It is shown that the main contribution to the backscattering is from the mirror reflection from the leading edge of such a wave, and the sharpness of the wave edge leads to the fact that the backscattering cross section of horizontally polarized radiation can exceed that of the vertically polarized radiation. Institute for Space Research, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 240–254, March 1999.     

Effektive Stoßquerschnitte bei Streuversuchen

Scattering experiments are often not performed with the ideal set-up consisting of a monochromatic beam and target particles at rest. This is, for instance, never the case in molecular beam scattering, which is of primary interest in this paper. Two arrangements are normally employed, one consisting of a gas chamber as target (case a), the other of a crossed beam, generally at right angles to the incoming beam (case b). In both cases the scattering particles have a Maxwellian velocity distribution. This means that in any such experiment an “effective cross section” is measured, which is an integral over cross sections for different collision velocities. Other similar integrals are needed, if one works with polarized beams and takes into account the fact that the cross section is angular dependent. A third type of integral is required, when the primary beam is not monochromatized, and one has to average over its velocity distribution too. The functions needed to interpret scattering experiments of all the types mentioned are given in this paper, as well as a table of values for the 24 most important of these functions.