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.     

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.     

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.     

Elastic and charge exchange scattering of pions from He

Elastic and charge exchange scattering of pions from ³He is studied using an optical potential in the momentum representation, which includes the second-order effect as well as the nucleon binding correction. These corrections are found to be appreciable but still not enough to resolve the discrepancy between theoretical calculations and recent experimental data on the reaction ³He(π⁻, π⁰)³H.     

Target excitation dependence of self-similar cascading rate in multihadron production process at 350 GeV

In the present work target excitation dependence of the self-similar cascading rate has been studied in detail in the framework of Levy stable law using the experimental data of pions obtained from π ^?-AgBr interactions at 350 GeV/c. TheLevy indices µ measured from the analysis fulfill the requirement of the Levy stable region 0 ? µ ? 2. The study gives an evidence of self-similar cascading mechanism responsible for multiparticle production. The different values of µ indicate different rates of cascading for different degrees of target excitation. Moreover, the values of universal scaling exponent (ν) obtained from Ginzburg-Landau theory indicate that no clear evidence of second-order phase transition has been found in the interaction.     

Pions interact with nuclei

This is a pedagogically oriented report about the interaction of pions with nuclei. The review is restricted to low and medium energy phenomena, i.e., to pion energies below 300 MeV. Pionic atoms, pion absorption and production, and the scattering around the (3,3) resonance are the main topics. The experimental data are interpreted within the frame of multiple scattering theory. The basic ideas are critically analysed and open problems are stressed.     

Multiple scattering of muons in beryllium

The defocussing and the depolarization of a high energy muon beam in a beryllium filter, often used to eliminate accompanying pions, have been studied. The quantum mechanical transport equation of Waldmann, which can also be used to describe the multiple scattering of Dirac particles, is solved with a distorted wave Born approximation. Calculations are done for both the Thomas-Fermi and the Hartree-Fock potential of the beryllium atom. It is shown that the Hartree-Fock potential leads to a less divergent beam. The depolarization of a longitudinally polarized muon beam in passage through a thin beryllium foil is also studied.     

Elastic and the 2+ inelastic scattering of high energy protons on12C and the alpha-particle model

The alpha-particle model has been applied to calculate the elastic and the 2⁺ inelastic angular distribution of 1 GeV protons on¹²C within the framework of Glauber multiple scattering theory. The results are compared with the recent experimental data and with some previous calculations. The model gives a fairly good account of the inelastic data and its predictions for the elastic scattering are essentially the same as those of the shell model.     

第二玻恩近似理论研究激光辅助e-Ar散射

在电子入射方向平行于激光场的极化方向这种特殊的散射模式下，应用第二玻恩近似(SBA)理论，分别利用含有极化势的静电屏蔽势和单纯的静电屏蔽势这两种原子势模型对激光场中电子-氩原子散射进行了研究，并与低频近似和实验数据进行了比较.结果表明，第二玻恩近似理论给出的结果与实验符合较好.另外，极化势在激光辅助电子-原子散射中起着重要作用. 关键词： 极化势 第二玻恩近似 微分截面 激光场     

Pulse broadening of enhanced backscattering from rough surfaces

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l≳λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Three-body coupling for electron impact ionization of helium in the perpendicular plane geometry

Dynamically screened three-Coulomb-wave (DS3C) model is applied to study single ionization of helium by 102 eV electron impact. Fully differential cross sections (FDCS) are calculated at different scattering angle of (8°, 10°, 15°, 20°) in the perpendicular plane asymmetric geometry. The results are compared with experimental data and theoretical predictions from a three-Coulomb wave function (3C) approach, convergent close-coupling calculation (CCC), as well as second-order distorted-wave Born method (DWB2). It is shown that three-body coupling effects are important for the perpendicular plane geometry.     

Emission in the final state in processes with the production of charged pions and light leptons

The Drell-Yan form is proposed for the decay widths of heavy quarks and cross sections for high-energy scattering with the production of charged pions and light leptons including radiative corrections in the final state in the leading logarithmic approximation. The corresponding spectral distributions are given in terms of the convolution of the cross section (decay width) in the Born approximation with the structure functions of pions and leptons. The pion structure function is given in the explicit form.     

Spectral Changes of Light Produced by Multiple Scattering from Space-Time Fluctuating Random Media under the Born Approximation

Changes in the spectrum of light scattered by space-time fluctuating random media are investigated theoretically within the accuracy of the second-order Born approximation, as a continuation of the previous paper [Opt. Commun. 123 (1996) 234]. Effects of multiple scattering on the resultant field are manifested by a number of illustrative examples. It is shown, in particular, that the spectrum of the scattered light to be observed under practical circumstances is distorted by the process of multiple scattering. Comparison between spectra of both single and multiple scattering lights is also presented in the framework of the dynamic scattering.     

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.     

A second-order vibrational model applied to the scattering of electrons and α-particles from 12C

Transition densities for monopole excitations and for virtual excitations are derived in the second-order vibrational model. Form factors for electron scattering calculated in the Born approximation and angular distributions for α-particle scattering, obtained in coupled channel calculations, are compared with experimental results for the elastic scattering and the inelastic scattering from the 2⁺ level at 4.44 MeV, the 0⁺ level at 7.65 MeV and the 3^? level at 9.64 MeV in ¹²C.     

The multiple scattering theory of phonons in mass disordered lattices

A version of the multiple scattering theory previously applied to the electronic problem of substitutional alloys is completed and modified in order to handle the problem of vibrations of general mass-disordered crystal lattices. The Born series is expressed in terms describing the scattering corrections to the appropriate effective medium. A new physical interpretation of the effective medium condition is given and the total partial summation of the Born series for the full scattering T-matrix is completed to the infinite order. The T-matrix is thus re-expressed in terms corresponding to resonant “ping-pong” scattering of renormalized phonons on all possible clusters of scattering centres. Confining to clusters of only limited number of scattering centres yields a set of successive approximations. The one-centre approximation for cubic crystals complies with the Taylor's selfconsistent procedure. A simple illustrative example in the two-centre approximation is solved and discussed.     

Ultrasoft x-ray Bremsstrahlung isochromatic spectra from 300-2000 eV electrons on Ar and Kr

For the first time the bremsstrahlung effect was studied experimentally in the spectral region of 6.5-10 nm with 300-2000 eV electron scattering on Ar and Kr atoms. The isochromatic curves displayed maxima at electron energies of approximately = 0.7 keV (Ar) and approximately =1 keV (Kr); their positions are almost independent of the radiation wavelength in the range studied. These experimental data cannot be treated in the framework of theory based on the first Born approximation. A phenomenological modification of the quasiclassical (soft-photon) approximation is proposed which gives a qualitative treatment of data.     

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.