An integrated model to simulate the scattering of ultrasounds by inclusions in steels

We present a study performed to model and predict the ultrasonic response of alumina inclusions in steels. The Born and the extended quasistatic approximations have been applied and modified to improve their accuracy in the framework of this application. The modified Born approximation, called "doubly distorted wave (D(2)W) Born approximation" allowing to deal with various inclusion shapes, has been selected to be implemented in the CIVA software. The model reliability has been evaluated by comparison with Ying and Truell's exact analytical solution. In parallel, measurements have been carried out upon both natural and artificial alumina inclusions.     

共面双对称条件下电子碰撞Ar原子单电离的一阶扭曲波Born近似

在共面双对称几何条件下,利用一阶扭曲波Born近似计算了中低能电子碰撞Ar原子(3p壳层电子)单电离的三重微分截面,并与最近的实验数据做了比较.结果表明,对于Ar原子,当入射电子能量比电离阈高40 eV以上,随着入射能量的增加,binary和recoil碰撞机理逐渐占据支配地位;在近阈能量范围,上述碰撞机理不再处于支配地位,扭曲效应明显.要完备地描述中低能入射条件下Ar原子的电子碰撞电离过程,理论模型必须同时考虑多种散射机理.     

Study of (e, 2e) process on potassium at 6 eV—60 eV above threshold in second-order Born approximation

The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for alkali target potassium at excess energies of 6 eV-60 eV. Comparing with the first-order DWBA calculations before, the present theoretical model improves the degree of agreement with experiments, especially for backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e, 2e) problems in low and intermediate energy range.     

Study of （e, 2e） process on potassium at 6 eV-60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation(DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target.Second-order DWBA calculations have been preformed to investigate the triple differential cross sections(TDCS) of coplanar doubly symmetric(e,2e) collisions for the alkali target potassium at excess energies of 6 eV-60 eV.Compared with the previous first-order DWBA calculations,the present theoretical model improves the degree of agreement with experiments,especially for the backward scattering angle region of TDCS.This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric(e,2e) problems in low and intermediate energy ranges.     

Distribution of backscattered intensity in the distorted Born approximation: Application to C-band SAR images of woodland

Abstract

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.     

Radiative corrections to very high energy electron-proton scattering

A “leading log” analysis of radiative corrections to inclusive ep scattering at HERA energies is presented. Neutral current weak interactions are considered at the level of the Born cross section as well as of the modifications of vertex and vacuum polarization parts. The leading log approximation has been also improved in the single hard and multiple soft photon emission by appropriate kinematical considerations. Some numerical results are presented for polarized electron and positron beams.     

Propagation of guided waves through weak penetrable scatterers

The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed.     

On the validity of some new acoustic scattering approximations

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.     

On the validity of some new acoustic scattering approximations

Abstract

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.     

A systematic comparison between born approximation and distorted wave Born approximation for inelastic electron scattering

The correction factors for Coulomb effects in inelastic electron scattering are given for electric quadrupole transitions. The cross sections in Born approximation and distorted wave Born approximation are calculated in the liquid drop model for electron energies between 20 and 80 MeV and nuclei up toZ=26.     

On the unitarization of the Born approximation

A new approximation for the elastic scattering transition matrix is suggested. This approximation satisfies the unitarity condition. A modified Born series is introduced which has this unitarized Born approximation as the leading term. The series is applied to the solvable case of scattering by a separable potential and is found to converge in a wider region of energies than that of the conventional Born series.     

An extended Rytov approximation and its significance for remote sensing and inverse scattering

The Born approximation has been shown by Wolf to be particularly convenient for formulating inverse scattering problems. The Rytov approximation is known to be more widely applicable than the Born approximation. We introduce an improvement that further increases the range of validity of the Rytov approximation. It transpires that our extension of the Rytov approximation is as convenient for inverse scattering as the Born approximation.     

Breakup of light nuclei within the modified distorted wave Born approximation

Reactions of the elastic breakup of loosely bound light nuclei are investigated in the scope of the distorted wave Born approximation, with deuterium breakup reactions used as an example. Some drawbacks of this approximation in calculating the breakup amplitude in the prior form are shown and their causes analyzed. We propose eliminating the drawbacks by employing a modified nucleus-nucleus potential in calculating the distorted wave functions of scattering in the exit reaction channel. The calculations are compared to the experimental data.     

Electron capture processes in ion-atom collisions

The development of the theory of electron capture processes in ion-atom collisions is reviewed in the present work. The formal theory of scattering is used to obtain the Born and the distorted wave Born series for the rearrangement scattering matrix. On the basis of these series, the applications of the first and second Born approximation, the OBK approximation, the DWBA and the Padé approximants to electron capture processes are discussed. The impulse approximation, the Faddeev method and the second order potential method are also explained. The results of the investigations of the high energy behaviour of the charge transfer cross section based on the Faddeev-Watson multiple scattering expansion are analysed.The methods of molecular and atomic eigenfunction expansions are presented and their relative merits discussed. The semi-classical treatment for determining the differential electron capture probability is reviewed. Results obtained in works utilising expansions in Sturmian, Gaussian and pseudo-state wave functions are also presented. An integral equation approach to the close coupling approximation is described. The field theoretic approach to investigate the electron capture process is discussed in the last section.The results obtained by different theoretical methods are compared with available experimental results.     

Positron scattering from hydrogen atom embedded in weakly-coupled plasmas

Elastic scattering of positrons from the hydrogen atoms in weakly-coupled plasmas has been studied using an expression for partial wave scattering amplitude that has been derived within the framework second order distorted wave Born approximation. The interactions among the charged particles in the plasma have been represented by Debye-Hückel potentials. A detailed study has been made on differential and total cross sections in the energy range 20–300 eV. To the best of our knowledge such a study on the differential and total cross sections for elastic positron-hydrogen collisions in a weakly-coupled plasma environment is reported for the first time in the literature.     

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.     

Differential cross sections for elastic and inelastic positron scattering from alkali atoms

We have investigated positron scattering from the alkali atoms lithium, sodium, potassium and rubidium, focusing on the calculation of differential cross sections for elastic scattering and impact excitation. The results obtained with the two-state and five-state close-coupling method as well as the first-order distorted wave Born approximation are compared with each other and with some selected results for electron scattering. Numerical problems due to lack of, or numerically inaccurate, calculation of partial waves with large angular momenta are solved through semi-empirical fitting/extrapolation procedures.     

双模激光场中电子-原子散射

在一阶玻恩近似的基础之上,本文首次在激光场的极化方向平行于入射电子的方向这种散射模式下,应用二阶玻恩近似理论对双模激光场中电子-氩原子散射的自由-自由跃迁过程进行了研究,并与一阶玻恩近似结果进行比较.结果表明,二阶玻恩近似理论在多模激光场中的应用也是比较成功的.     

Elastic and inelastic scattering of 270 MeV3He particles from58Ni,90Zr,116Sn and208Pb

Differential cross-section angular distributions for the elastic scattering of 270 MeV³He particles from⁵⁸Ni,⁹⁰Zr,¹¹⁶Sn and²⁰⁸Pb have been measured. Optical model analysis of the cross-sections has yielded the optical model parameters for³He particles at 270 MeV. Angular distributions have also been measured for the inelastic excitation of the low-lying levels in the above mentioned nuclei. A collective model analysis using the distorted wave Born approximation (DWBA) of these cross-sections with the distorted waves generated by the optical model parameters determined from the elastic scattering analysis, has yielded the reduced transition probability (B(EL)) values consistent with those reported in the literature.     

Parity non-conservation in low energy scattering of nucleons by light nuclei: (I). Theoretical framework

The low energy scattering of nucleons by ²H, ³He and ⁴He are analyzed for parity non-conserving effects. The asymmetry in the total cross section of longitudinally polarized projectiles is formulated in terms of the optical theorem and a distorted wave Born approximation. For two nucleons at low energies it is only necessary to consider l = 0 to l = 1 matrix elements of the weak nucleon-nucleon potential. The asymmetries in the scattering from nuclear targets are related to the parameters of an effective weak nucleon-nucleon potential, so that they may be used to help differentiate between various proposed theoretical potentials.