Improving the Born approximation for the scattering of ultrasound in elastic solids

It has recently been demonstrated that the Born approximation for predicting the scattering response of flaws can be improved through the use of simple modifications called the "doubly distorted Born approximation". In this paper the doubly distorted Born approximation itself is modified with phase and amplitude corrections that further improve the Born scattering results for isotropic elastic media. The reliability of this new modification of the Born approximation has been evaluated by comparison with the exact solution for spherical inclusions obtained with the method of separation of variables. Unlike the ordinary Born approximation which works well only for very weak scattering inclusions, our modification of the doubly distorted Born approximation gives improved scattering results for both weak and strong scattering inclusions.     

Comparison of eikonal-Born series and modified Gluaber approach for the study of elastic electron-hydrogen scattering

Elastic electron-hydrogen scattering at medium and high energies has been analysed in eikonal-Born series and modified Glauber approach forE _i ≥ 50 eV. We have used closed form expressions for evaluating the second Born term in the fixed scatterer approximation and for higher order terms of Glauber-eikonal series. The exchange effect has also been included via Glauber-Bonham-Ochkur type procedure. The fixed scatterer approximation calculations are compared with results obtained using other approximations for the second Born term available in the literature. The results compare fairly well with experimental data.     

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.     

Theoretical calculation of the triple differential cross sections of the 2p orbital of argon in a coplanar highly asymmetric（e,2e） reaction

The triple differential cross sections of the 2p electron of argon in a coplanar highly asymmetric geometry have been calculated with the modified distorted wave Born approximation (DWBA) and the target Hartree－Fock approximation methods. The damping polarization of the semi-classical short-range potentials and the M_ee factor are included in the distorting potentials of the modified DWBA. Theoretical results are compared with a recent experiment. The dynamic mechanism of inner shell ionization in a coplanar highly asymmetric geometry (e, 2e) reaction are also discussed.     

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.     

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.     

共面不对称条件下Ar原子(e,2e)反应的三重微分截面

采用修正的扭曲波玻恩近似(DWBA)方法,计算了共面、大能量损失和小动量转移这一特殊几何条件下电子碰撞Ar(3p6)(e,2e)反应的三重微分截面.理论方法对(e,2e)反应过程近程极化势进行了修正,并引入Gamow因子表示后碰撞相互作用(PCI).将计算结果与实验结果、标准DWBA计算结果及Gamow因子修正后的DWBA-G计算结果进行了比较,发现极化效应起着重要的作用.     

Mehrfachstreuung von Elektronen im Energiebereich von 0,52 bis 2,0 MeV

The plural nuclear scattering of electrons with kinetic energies of 0.52 MeV up to 2.0 MeV has been measured for angles between 0° and 20°. Pb, Ag and Al foils of various thicknesses (mean number of collisions between 1 and 21) had been used as targets. The experimentally derived angular distribution of the scattered electrons has been compared with a numerical computation byKeil, Zeitler andZinn based on theMolière theory of plural and multiple scattering and his approximation of the single scattering law. His corrected values of the shielding angle and the mean number of collisions describe the distribution of the scattered electrons better than the original ones derived from a Born approximation calculation. The intensity of the remaining unscattered electrons must be calculated with the Born approximation value for the mean number of collisions in order to obtain agreement with the experiment.     

Multiphonon resonances in the Debye-Waller factor of atom surface scattering

He atom surface scattering by dispersionless phonons is treated employing coupled channel (CC) calculations. At low energies, they predict a behavior opposite to perturbative Born or "exponentiated" Born approximation: strong resonant phonon stimulated elastic and inhibited inelastic scattering. The corresponding resonances have not been observed in earlier CC results since these have considered only the temperature dependence of the Debye-Waller factor at higher energy or omitted the attractive well. The resonances can be interpreted in terms of bound states in the attractive well with several excited vibrational quanta. They may be observable for, e.g., He scattering by a cold Xe/Cu surface.     

类硼离子的电子碰撞电离截面

运用扭曲波玻恩交换近似对处于Hartree-Fock基态的类硼离子的电子碰撞直接电离截面进行了计算。电离过程中直接电离与交换电离振幅的干涉有重要的贡献。研究结果表明“自然相因子”近似比“最大干涉”近似要好。后者用于其它离子种类的计算与实验符合很好。同Moores等人的Coulomb-Born近似计算相比较,我们的计算结果与现有的实验数据符合有改进。 关键词：     

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.     

Xe(4d~(10))(e,2e)反应三重微分截面的理论研究

采用修正后的扭曲波玻恩近似理论,计算了共面不对称几何条件下Xe(4d~(10))(e,2e)反应的三重微分截面.散射电子能量为1000 eV,敲出电子能量为20 eV,散射电子角度分别固定在2°,4°和7.5°.理论计算与Avaldi等人的实验结果和扭曲波玻恩近似理论计算进行了比较,发现出射电子之间的后碰撞相互作用较弱,极化效应在反应过程中起着重要作用.     

Calculation of the intensity of Touschek electrons in the VEPP-4M storage ring

Formulas for calculating the intensity of intrabeam scattering of electrons in the Born approximation for the one- and two-dimensional collision models have been obtained for the nonrelativistic and relativistic cases. The Baier-Katkov-Strakhovenko two-dimensional relativistic model with Coulomb corrections has been analyzed. Formulas in the ultrarelativistic limit have been obtained using this model. Different models have been compared. The intensities of Touschek electrons and the polarization contribution have been calculated under the conditions of the detection of scattered particles at the VEPP-4M storage ring. The calculations have been compared to experimental data.     

Elastic scattering of electrons by hydrogen atom in a laser field

The cross-sections for the elastic scattering of electrons by hydrogen atoms in the presence of a laser field have been calculated in the Glauber and the Born approximations. The Born approximation has been found to underestimate the cross-sections and the increase of the intensity of the electromagnetic field is found to lower the cross sections.     

Virtual nuclear excitation corrections to elastic electron scattering from 40Ca

The virtual nuclear excitation (dispersion) corrections to elastic electron scattering from ⁴⁰Ca have been calculated in second-order Born approximation. A model that can reproduce the whole inelastic response surface is employed for the nuclear currents that enter. The dispersion correction, expressed relative to the first Born result, is dependent only on the nuclear Fermi momentum. When the intermediate nuclear states are summed (without using closure) through the quasi-elastic scattering region, the corrections are found to be small (about 3%). However, these should be included in analyzing future data with better experimental accuracy. For the first time, the effect of isobar excitation on the dispersion correction has been examined; because of the questionable validity of the approximations in this case, no definite conclusion can be drawn.     

Effect of polarization of shell-model states in reaction calculations for 40Ca(16O, 15N)41Sc1f72

The reaction ⁴⁰Ca(¹⁶O, ¹⁵N)⁴¹Sc_g.s. has been investigated in the context of a model where the final single-particle state in ⁴¹Sc was modified or polarized due to the proximity of the other nucleus. Calculations, performed with the finite-range distorted waves Born approximation code KUNDRY, using two-centre shell model wavefunctions, demonstrate that this polarization produces effects on the cross section which indicate a resolution to some discrepancies between previous DWBA predictions and experiment.     

Theoretical calculation of triple differential cross sections of 3s orbital of argon in coplanar symmetric （e, 2e） reaction

The triple differential cross section for the low-energy electron impact ionization of inner-valence 3s orbital of argon has been calculated using the modified distorted wave Born approximation in coplanar symmetric energy-sharing geometry. Satisfactory agreement between theory and experiraent is achieved when the polarization and post-collisional interaction (PCI) are included in the calculations. It is shown that the polarization and PCI effects play a very important role in the case of argon at low incident energies.     

Long-range Coulomb forces in DIS: missed radiative corrections?

The Born approximation, one photon exchange, used for DIS (deep inelastic scattering) is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Zα is not a small parameter. So far, these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case also the cross-section is modified. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than “swept under the carpet”. The importance of these radiative corrections is questioned in the present paper. We show that, in the simplest case of a constant hadronic current, the Coulomb corrections provide a phase to the Born amplitude, therefore the cross-section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Zα, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons, we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation. Received: 16 May 2001 / Accepted: 4 July 2001     

共面不对称条件下低能电子碰撞电离Ar(3p)的三重微分截面

采用修正的扭曲波玻恩近似方法, 在共面不对称几何条件下, 计算了能量为70.8 eV电子与Ar(3p)碰撞电离的(e, 2e)三重微分截面, 并与最新实验数据进行了比较. 结果表明电子交换效应和后碰撞相互作用在低能电子碰撞的(e, 2e)过程中起着重要作用. 关键词： (e,2e)三重微分截面 扭曲波玻恩近似 后碰撞相互作用 电子交换效应