Eikonal expansion in electron scattering

We extend a previously developed eikonal expansion method to the case of high-energy electron scattering from dynamic nuclei. Nuclear degrees of freedom can be included either by a DWBA-like expansion or by neglecting the nuclear excitation energies. The latter approach is considered in detail and applied to the elastic and inelastic scattering from deformed nuclei. The impact parameterT-matrix is calculated by diagonalizing the inelastic zeroth-order and first-order eikonal phases in the subspace of the nuclear rotational levels; static eikonal phases are included up to second order. For¹⁵²Sm,¹⁵⁴Sm coupled-channel calculations including three and four rotational states show large multi-step effects for the 0⁺→4⁺ and the 0⁺→6⁺ excitations compared to DWBA results.     

Eikonal expansion in electron scattering: I. Elastic scattering

A systematic eikonal expansion for the scattering of high-energy electrons from nuclei is derived which starts from the iterated Dirac equation. The resulting scattering amplitude is written in an impact parameter representation depending on eikonal phases which are proportional to inverse powers of the energy. The first two correction terms to the leading Glauber-Baker amplitude are calculated. For a Coulomb potential they agree with a sinθ-expansion of the relativistic Coulomb scattering amplitude. In the case of scattering from an extended charge distribution at sufficiently high energies numerical partial wave calculations are accurately reproduced.     

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order 1/k ², where k is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.     

Eikonal description of quantal scattering

Elastic and inelastic quantal scattering is described by a theory in which the contribution of a range of impact parameters to the scattering amplitude is determined by a phase integral (“eikonal”) which is integrated along a real curved “quantal” trajectory. This amplitude reduces to the Glauber expression in the high-energy, forward-angle limit, and to the usual semiclassical amplitude in the classical limit. The formulation can be applied to the study of heavy-ion scattering. The quantal trajectories are investigated analytically for the case of Coulomb scattering. A numerical analysis of elastic ¹⁶O¹⁶O scattering is carried out. The results show appreciable improvement as compared with the Glauber 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.     

Eikonal approximation in the theory of X-ray interferometer

On the basis of eikonal approximation a theory of X-ray moiré formation is presented in the case where deformations are present in all three plates of the interferometer. The role of each plate of the interferometer in the process of moiré formation is revealed. The theory can be applied for the general case of weak deformations.     

Coulomb corrections for coherent electroproduction of vector mesons: Eikonal approximation

Virtual radiative corrections due to the long-range Coulomb forces of heavy nuclei with charge Z may lead to sizeable corrections to the Born cross-section usually used for lepton-nucleus scattering processes. An introduction and presentation of the most important issues of the eikonal approximation is given. We present calculations for forward electroproduction of rho-mesons in a framework suggested by the VDM (vector dominance model), using the eikonal approximation. It turns out that Coulomb corrections may become relatively large. Some minor errors in the literature are corrected.Received: 3 October 2003, Revised: 2 December 2003, Published online: 6 July 2004PACS: 25.30.-c Lepton-induced reactions - 25.30.Rw Electroproduction reactions - 13.40.-f Electromagnetic processes and properties - 25.30.Bf Elastic electron scattering     

The Coulomb sum for electron scattering in the relativistic random phase approximation

The Coulomb sum value for electron scattering is estimated using the relativistic random phase approximation (RPA) in the field theory for nuclear matter. RPA correlations due to σ-, ω- and ϱ-meson exchanges reduce the sum value of the relativistic Hartree approximation by about 15–20%.     

Recoil corrections to elastic electron scattering in the Breit approximation

Recoil corrections to the cross sections for elastic electron scattering from spin-0 nuclei are investigated in the Breit approximation. The form of the scattering amplitude in first- and second-Born approximation is investigated in detail using time-dependent perturbation theory, and it is found that the center-of-mass (CM) frame is particularly convenient to work in. Transformation equations relating the lab and CM frames are developed. Those parts of the second-Born amplitude which correspond to the Breit amplitude are isolated, and the Breit equation with the electromagnetic Breit interaction is investigated in detail. Corrections to the scattering cross sections which are inversely proportional to the nucleus mass (recoil corrections) are calculated. Numerical results are presented for the particular case of ¹⁶O.     

Configuration mixing and elastic magnetic electron scattering from nuclei

The role of configuration mixing in the analysis of recent elastic magnetic electron scattering experiments on ⁴⁹Ti, ⁵⁹Co, ⁸⁷Sr and ⁹³Nb is examined. In particular the dependence of the rms radius of the valence nucleon extracted from such analyses on the detailed nuclear configurations used is studied. In addition, the effects of meson-exchange currents together with configuration mixing are discussed. It is found that configuration mixing does play a significant role and that high-precision studies of elastic magnetic electron scattering should proceed beyond the framework of the extreme single-particle model.     

关联电子体系中电子和磁的拉曼散射

周期结构的晶格振动和分子的振动或转动谱,可以看作材料的特征指纹,拉曼散射正是探测这些振动的非常灵敏和有效的技术,因此它已经被广泛地应用到基础研究和工业生产的各个方面.而原则上,通过固体中的自由载流子或自旋与光的非弹性散射过程,人们也可以获得关于电子和磁激发的重要信息.文章对电子和磁的拉曼散射基本概念作了简要介绍,并对一些关联电子体系中的拉曼实验作了简要综述.特别是在非常规超导中,拉曼散射在确定超导能隙的大小和各向异性以及配对对称性等方面发挥了独特的作用.     

关联电子体系中电子和磁的拉曼散射

周期结构的晶格振动和分子的振动或转动谱,可以看作材料的特征指纹,拉曼散射正是探测这些振动的非常灵敏和有效的技术,因此它已经被广泛地应用到基础研究和工业生产的各个方面.而原则上,通过固体中的自由载流子或自旋与光的非弹性散射过程,人们也可以获得关于电子和磁激发的重要信息.文章对电子和磁的拉曼散射基本概念作了简要介绍,并对一些关联电子体系中的拉曼实验作了简要综述.特别是在非常规超导中,拉曼散射在确定超导能隙的大小和各向异性以及配对对称性等方面发挥了独特的作用.     

Eikonal regime of gravity-induced scattering at higher energy proton colliders

We compute transplanckian parton scattering in flat extra-dimensional theories at the LHC and at the recently discussed high-energy upgrade (HE LHC). We report new leading-order calculations of the QCD background. We apply appropriate cuts to satisfy the necessary conditions for the eikonal approximation to be valid while at the same time maximising the signal to background ratio at LHC energies. We study the computability of the eikonal signal and consider the effect of a possible 33 TeV high-energy upgrade to the LHC, which serves to extend the calculable region and to enhance the signal to background ratio.     

Eikonal approximation in the theory of energy loss by fast charged particles

Energy losses in fast charged particles as a result of collisions with atoms are considered in the eikonal approximation. It is shown that the nonperturbative contribution to effective stopping in the range of intermediate impact parameters (comparable with the characteristic sizes of the electron shells of the target atoms) may turn out to be significant as compared to shell corrections to the Bethe-Bloch formula calculated in perturbation theory. The simplifying assumptions are formulated under which the Bethe-Bloch formula can be derived in the eikonal approximation. It is shown that the allowance for nonperturbative effects may lead to considerable (up to 50%) corrections to the Bethe-Bloch formula. The applicability range for the Bethe-Bloch formula is analyzed. It is concluded that calculation of the energy loss in the eikonal approximation (in the range of impact parameters for which the Bethe-Bloch formula is normally used) is much more advantageous than analysis based on the Bethe-Bloch formula and its modifications because not only the Bloch correction is included in the former calculations, the range of intermediate impact parameters is also taken into account nonperturbatively; in addition, direct generalization to the cases of collisions of complex projectiles and targets is possible in this case.     

Higher-order modified Born approximation for potential scattering in the presence of a strong magnetic field

Summary The total cross-section for potential scattering in the presence of a strong magnetic field presents singularities and exhibits giant growth (cyclotron resonances) at values of the incident particle energy exactly matching the differences between the initial-and final-state Landau levels. In this paper (in cylindrical coordinates) a higher-order modified Born series has been derived that can be summed at all orders giving a nondivergent total cross-section at the Landau thresholds.     

M5 and higher magnetic moments in elastic electron scattering

We consider the feasibility of determining the higher nuclear ground state magnetic moments through elastic electron scattering. Theoretical and experimental results are presented for the M5 moment of ₁₃²⁷Al and the M9 moment of ₈₃²⁰⁹Bi.