A practical cross-section for scattering from rough surfaces at very low grazing angles in both the forward and backward directions

In this paper we develop an extension of the small slope approximation (SSA) for scattering from randomly rough Dirichlet surfaces, which includes some multiple scattering. This extension is designated by SSA+. We focus on scattering at very low grazing angles where multiple scattering of both the incident and scattered fields is of importance. Numerical results for the SSA+ bistatic scattering cross-section for very low forward grazing angles are presented using the Gaussian roughness spectrum and for both very low forward and very low backward grazing angles using the Pierson–Moskowitz and modified power law spectra. The results are restricted to an angle of incidence of 80°. It is shown that when the lowest-order SSA gives reasonably accurate results, the SSA+ increases the accuracy up to at least the final 0.2° of grazing in the forward direction. In the backward direction, the SSA+ gives good results for the Pierson–Moskowitz spectrum, but the results are less dramatic.     

Elastic scattering of an electron on the Coulomb potential with a cut-off

The partial-wave method is used to study the elastic scattering of electrons on the Coulomb potential with a cut-off. There is considerable discrepancy between the present results and those obtained by means of the Born approximation and the classical method. At a given specific energy, the cross section exhibits a maximum. This due to the appearance of maxima in the differential cross section in both the forward and the backward direction.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey-Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.     

Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates

This paper presents a theoretical and finite element (FE) investigation of the scattering characteristics of the fundamental anti-symmetric (A₀) Lamb wave at delaminations in a quasi-isotropic (QI) composite laminate. Analytical models based on the Mindlin plate theory and Born approximation are presented to predict the A₀ Lamb wave scattering at a delamination, which is modelled as an inhomogeneity, in an equivalent isotropic model of the QI composite laminate. The results are compared with FE predictions, in which the delamination is modelled as a volume split. The equivalent isotropic model and QI composite laminate are used to investigate the feasibility of the common theoretical approach of modelling the delamination as the inhomogeneity. A good correlation is observed between the theoretical solutions and FE results in the forward scattering amplitudes, but there exists a larger discrepancy in the backward scattering amplitudes. The FE results also show that the fibre direction of the outer laminae has a pronounced influence on the forward and backward scattering amplitudes, which is not predicted by the analytical models.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

Abstract

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second–order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.     

«Buckingham» approximants to physical laws

Summary The typical problem is addressed of system and process modelling depending on a large number of variables. Demonstration is given that the number of independent variables can be dramatically reduced, by a modified application of Buckingham's theorem of dimensional analysis, resulting in a simplified formulation of the problem in terms of a limited number of dimensionless arguments. This simplified formulation eventually leads, by interpolation of numerical data, to the derivation of practical approximants to the physical laws governing the system or process. This approach is demonstrated, in case of electron scattering, through a general layer in the elastic regime, as modelled by Monte Carlo methods. In particular, a single dimensionless quality factor is introduced, allowing remarkable simplification both in forward and backward scattering analysis. Hence, Buckingam approximants are derived, effectively describing the scattering by universal laws, applicable to all elements of the periodic table and all variations of electron energy and layer thickness, in the ranges 5 to 150 keV and 1 to 3000 nm. The proposed method may be considered as a physical approximation, compared to purely mathematical methods, such as for example Padé approximants. As a consequence, the method is understandably highly effective, and may be extensively applied to all systems and processes susceptible to being described by mathematical modelling.     

Quasiclassical green function in an external field and small-angle scattering processes

A representation is obtained for the quasiclassical Green functions of the Dirac and Klein-Gordon equations allowing for the first nonvanishing correction in an arbitrary localized potential which generally possesses no spherical symmetry. This is used to obtain a solution of these equations in an approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not reduce to the Green function obtained in the eikonal approximation and has a wider range of validity. This is illustrated by calculating the amplitude of small-angle scattering of a charged particle and the amplitude of Delbrück forward scattering. A correction proportional to the scattering angle was obtained for the amplitude of charged particle scattering in a potential possessing no spherical symmetry. The real part of the Delbrück forward scattering amplitude was calculated in a screened Coulomb potential.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

A two-way marching coupled-mode method for range-dependent propagation

##正##An efficient,accurate,and numerically stable coupled-mode solution is presented for acoustic propagation in a range-dependent waveguide.This method is numerically stable due to the appropriately normalized range solutions introduced in the formulation.In addition,by combining a forward marching and a backward marching,this method provides accurate solutions for range-dependent propagation problems,especially those characterized by large bottom slope angle and/or high impedance contrast between water and the bottom.Furthermore,this two-way solution also provides high efficiency,which is achieved by applying the single-scatter approximation.Numerical examples are also provided to demonstrate the efficiency,accuracy, and stability of this method.     

Variable amplitude equations for one-dimensional scattering

Nonlinear first-order equations, similar to Calogero's equations, are derived for the forward and backward one-dimensional scattering amplitudes. In particular, the even potential case yields two uncoupled equations for the even and odd parity phase shifts. The present approach provides a fast and accurate means for the numerical solution of one-dimensional scattering problems. It also has many analytic merits, some of which are discussed. The connection between one-dimensional and three-dimensional high-energy scattering is reviewed. It is demonstrated that in the one-dimensional case, a slightly modified WKB wavefunction provides an excellent approximation to the exact wavefunction in the shortwave limit. In this limit, additivity of phase shifts for nonoverlapping static potentials is satisfied.     

Backscattering response from periodic spatial patterns in random media

Abstract

In wave-based remote sensing or radio-location of distant objects in a random medium, a high-frequency electromagnetic wave is scattered by object discontinuities, and portions of the scattered radiation can traverse the same random inhomogeneities as the initial incident field. The statistical dependence of the forward–backward travelling events results in an anomaly in the backscattered intensity pattern that carries information about the scattering object. The quality of this information depends on the ability to resolve the fine-structure elements. In this work we investigate the resolving properties of periodic spatial objects by using the random propagators of the stochastic geometrical theory of diffraction.     

Quantum-orbit theory of low-energy above-threshold ionization on and off axis

Intense-laser-induced above-threshold ionization of a bound electron into continuum states with low energy is investigated in the context of the strong-field approximation that allows for one act of rescattering of the revisiting electron. The quantum orbits for forward and backward scattering are evaluated and generalized to arbitrary scattering angles. The velocity map of the liberated electron exhibits the well-known low-energy structure as well as other features off the polarization axis.     

DUV scattering measurements as a tool for characterization of UV-optical surfaces

A sensitive total-scattering measurement setup for the DUV spectral range is presented, which allows precise determination of both forward and backward scatter losses from optical components for excimer lasers with a sensitivity below 10 ppm for 248 nm and 50 ppm for 193 nm. Scattering from several different coated and uncoated DUV optical surfaces was monitored. For uncoated samples, the backward scatter losses are in good agreement with the predictions of scalar scattering theory, indicating that in this case scattering is mainly determined by surface effects. Although forward and backward scatter losses are of the same order of magnitude for uncoated samples, they differ by up to two orders of magnitude for high-reflection- and by one order of magnitude for anti-reflection-coated samples. The experimental data demonstrate that the anti-reflection coatings suffer from substantial losses due to forward scattering, whereas backward scattering is the predominant loss channel for high-reflection coatings. In addition, the strong influence of defects and impurities on the total scattering is demonstrated. Received: 5 June 2000 / Accepted: 6 June 2000 / Published online: 13 September 2000     

Phase diagram of quasi-one-dimensional metals and superconductivity in the (TMTSF)2X compounds

The phase diagram of a quasi-one-dimensional metal is derived for a system with interchain tunneling. Retarded and nonretarded forward and backward scattering interactions are included. We show that singly charged acceptor molecules produce a potential along the conducting chains which leads to a retarded umklapp scattering. This umklapp scattering depends strongly on the phonon frequency and can explain the crossover of spin density wave to superconductivity as function of pressure as observed in (TMTSF)₂X compounds.     

Triple differential cross section in (e, 2e) collisions for sodium in a coplanar symmetric geometry

The triple differential cross sections for (e, 2e) ionization of sodium in a coplanar symmetric geometry have been studied in distorted wave Born approximation with the modified semiclassical exchange potential. The present calculations improve the agreement between the theoretical and experimental results. The post-collision interaction and target polarization effects have also been studied. In addition, the variation trends of the shape and ratio for the forward and backward scattering peaks have been discussed. Besides, the small bump observed between these two peaks has been analyzed by the interaction between active electron and passive electrons.     

Real-time propagators at finite temperature and chemical potential

We derive a form of spectral representations for all bosonic and fermionic propagators in the real-time formulation of field theory at finite temperature and chemical potential. Besides being simple and symmetrical between the bosonic and the fermionic types, these representations depend explicitly on analytic functions only. This property allows for a simple evaluation of loop integrals in the energy variables over propagators in this form, even in the presence of chemical potentials, which is not possible for their conventional form.     

高效率受激喇曼散射源

本文报道在有机溶液(CH₃)₂SO中,用宽带5314埃激光泵浦,得到强6296埃斯托克斯相干受激喇曼辐射的实验。在中等泵浦功率密度下,受激喇曼斯托克斯辐射前向波能量转换效率达38％,观察到了后向斯托克斯受激辐射,后向波强度是前向散射波强度的80％,测量了前向散射的增益为2.5×10^-3厘米/兆瓦,测量了前向、后向散射光束的空间分布。论证了后向散射光束方向性的改善。 关键词：