First-order Eikonal Approximation Research Articles

Second-order eikonal corrections for [formula omitted

The first-order eikonal approximation is frequently adopted in interpreting the results of A(e,e′p) measurements. Glauber calculations, for example, typically adopt the first-order eikonal approximation. We present an extension of the relativistic eikonal approach to A(e,e′p) which accounts for second-order eikonal corrections. The numerical calculations are performed within the relativistic optical model eikonal approximation. The nuclear transparency results indicate that the effect of the second-order eikonal corrections is rather modest, even at Q2≈0.2 (GeV/c)2. The same applies to polarization observables, left–right asymmetries, and differential cross sections at low missing momenta. At high missing momenta, however, the second-order eikonal corrections are significant and bring the calculations in closer agreement with the data and/or the exact results from models adopting partial-wave expansions.

Effects of E2 and E1–E2 Interference on Coulomb Dissociationof 19C

We investigate the effects of higher order multipole transitions, inparticular electric quadrupole (E2) and E1–E2 interference, on theCoulomb dissociation of 19C within the framework of the firstorder eikonal approximation. The sensitivity of the total Coulombbreakup cross section and the longitudinal momentum distribution of thecore fragment to these effects are checked. The breakup occurspredominately through the dipole transition and the contribution of E2transition to the total cross section is found to be within the rangefrom 1 to 3% of that of E1. It is further observed that the E1–E2interference term contributes nothing to the integrated cross section.On the other hand, the longitudinal momentum distribution is observedto be insensitive to the E2 transition while the E1–E2 interferenceintroduces a small asymmetry in its shape.

Quantum-mechanical effects on eikonal cross section for elastic electron–ion collisions in dense high-temperature plasmas

The eikonal method is applied to investigate quantum-mechanical effects on elastic electron–ion collisions in dense high temperature plasmas. An effective pseudopotential model taking into account both quantum-mechanical effects and plasma screening effects is applied to describe the electron–ion interactions in dense high-temperature plasmas. The straight-line trajectory method is applied to the path of the projectile electron in order to investigate the variation of the eikonal cross section as a function of the impact parameter, thermal de Broglie wavelength, Debye length, and projectile energy. In the first-order eikonal approximation, the quantum-mechanical effect reduces the elastic electron–ion scattering cross section. It is also found that the quantum mechanical effect is increased with increasing the projectile energy.

Elastic electron–ion collisions in a Lorentzian plasma

Plasma screening effects on elastic electron–ion collision processes in a Lorentzian (kappa)-distribution plasma are investigated using the eikonal method. The electron–ion interaction potential is obtained by introducing a plasma dielectric function εκ. The semiclassical straight-line trajectory method is applied to the path of a projectile electron in order to investigate the variation of the eikonal phase as a function of impact parameter and spectral index κ. In the first-order eikonal approximation, the dynamic plasma screening effect on the eikonal phase is found to be a static screening effect, and depends only on the Debye length and spectral index. The position of the maximum of the differential elastic eikonal cross-section recedes from the ion core with increasing spectral index. The plasma screening effect on the eikonal cross-section increases with decreasing spectral index.

Plasma screening effects on eikonal phase for electron-ion elastic collisions in weakly coupled plasmas

Eikonal approximation is applied to investigate elastic electron-ion collisions in weakly coupled plasmas. Plasma screening effects on eikonal phase are investigated for eikonal differential elastic scattering cross sections. The electron-ion interaction potential in weakly coupled plasmas has been obtained by the introduction of the longitudinal plasma dielectric function. The semiclassical straight-line trajectory method is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase as a function of the impact parameter and the plasma parameters. In the first-order eikonal approximation, the dynamic plasma screening effect is identical to the static screening effect obtained by the Debye–Hückel potential. The eikonal differential elastic cross section substantially decreases with an increase in the projectile energy and increases as the plasma screening effect decreases through the Debye length. The plasma screening effects are more significant for large impact parameters.

First-order eikonal approximation for the elastic scattering of 800 MeV/c pions from 12C and 40Ca nuclei.

We have extended the first-order eikonal model formalism to include charged pions scattering on nuclei. It has been applied satisfactorily to elastic angular distributions of 800 MeV/c pions scattering from $^{12}\mathrm{C}$ and $^{40}\mathrm{Ca}$ nuclei. \textcopyright{} 1996 The American Physical Society.

Elastic scattering of electrons from atomic helium in the second-order eikonal approximation

The authors use Wallace's second-order eikonal approximation, (WSOEA, 1973) to analyse the elastic scattering of electrons from helium at incident energies of 100, 200 and 500 eV. The predictions of the WSOEA are compared with those of the partial-wave calculation and the results obtained in Glauber's first-order eikonal approximation (1959).

Elastic scattering of electrons and positrons from H and Ar in the second-order eikonal approximation

Wallace's (WSOEA) second-order eikonal approximation is used to calculate elastic differential cross sections for e-or+-H and e-or+-Ar scattering at 100 and 500 eV in the angular range 0-20 degrees . The predictions of the WSOEA are compared with those of the partial-wave calculation (PWC), in addition to the results obtained in the first Born approximation (FBA) and Glauber's first-order eikonal approximation (FOEA). The WOSEA shows a definite improvement upon the FBA and the FOEA and yields cross sections in good agreement with the PWC results.

Elastic scattering of electrons from Ar and Kr in the second-order eikonal approximation

We report the first application of Baker's second-order eikonal approximation (SOEA) to atomic collisions and compare the predictions of SOEA with those of Glauber's first-order eikonal approximation (FOEA). The SOEA takes into account amplitude modulation, in addition to phase modulation of the incoming plane wave. In the case of elastic scattering of electrons from argon and krypton, it is found that the second-order correction term influences to a large extent the angular distribution of scattered electrons. In the intermediate-and high-energy range it is seen that the SOEA gives much better agreement than the FOEA with the staticfield calculation of Fink and Yates.

Second-Order Eikonal Approximation for Potential Scattering

An eikonal approximation for potential scattering at high energies is derived to second order in $\frac{1}{k}$ for the Schr\"odinger equation. The procedure is based on the same assumptions and restrictions introduced by Glauber, except that the derivation is carried one order further. Whereas Glauber's solution provides for phase modulation of the incoming plane wave, the second-order eikonal approximation, in addition to amending the phase term, turns out also to include an amplitude modulation factor. This approximation, which is the result of maintaining the original calculation to higher order, differs in general from the perturbation correction by Wallace of Glauber's first-order eikonal approximation, although both reduce to the same correct solution for the special case of Coulomb scattering.