Coulomb corrections for quasielastic scattering: eikonal approximation

Aste, Andreas; Hencken, Kai; Jourdan, J.; Sick, I.; Trautmann, D.

doi:10.1016/j.nuclphysa.2004.08.001

Cited by 12 publications

(31 citation statements)

References 34 publications

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“…At the energies in the present experiment, the Effective Momentum Approximation (EMA) is a good approximation [49,50,51] to the exact calculation (52]. We apply the correction as outlined in [50], by adding an energy boost to the incoming and outgoing electron energy and calculate the change in the cross section.…”

Section: Coulomb Correctionsmentioning

confidence: 99%

Precise Measurement of the Nuclear Dependence of Structure Functions in Light Nuclei

Seely

2006

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The EMC effect has been with us for over 20 years. During this time, the nuclear dependence of the structure functions, and therefore the underlying quark distributions, has been studied with much success. However, the bulk of the experimental effort has been to measure the effect in heavy nuclei where it has the same zBj dependence and differs only in magnitude. Calculations predict large differences in both the magnitude and zBj-dependence of the EMC effect in 3 He and 4He and precise measurements of the EMC effect in these nuclei could be used to distinguish between existing models. E03-103 measured the inclusive electron scattering cross-section on 1 H, 2 H, 3 He, and 4He, as well as the heavier targets Be, C, Cu, and Au. This thesis describes the experiment in detail and presents results for 3 He, 4He, and carbon. These data provide the first measurement of the EMC effect in 3 He above xBj > 0.4, and improve upon the existing measurement of the effect in 4He.

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Section: Coulomb Correctionsmentioning

confidence: 99%

Precise Measurement of the Nuclear Dependence of Structure Functions in Light Nuclei

Seely

2006

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“…However, these calculations are cumbersome and difficult to control by people who were not directly involved in the development of the respective programs. Early DWBA calculations for 12 C and 40 Ca were presented in [11] Various approximate treatments have been proposed in the past for the treatment of Coulomb distortions [12,13,14,15,16,17,18,19], and there is an extensive literature on the so-called eikonal approximation [20,21,22,23,24,25,26]. At lowest order, an expansion of the electron wave function in αZ, where α is the fine-structure constant and Z the charge number of the nucleus, leads to the well known effective momentum approximation (EMA) [27], which plays an important role in experimental data analysis and which will be explained below.…”

Section: Introductionmentioning

confidence: 99%

Coulomb distortion of relativistic electrons in the nuclear electrostatic field

2005

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Continuum states of the Dirac equation are calculated numerically for the electrostatic field generated by the charge distribution of an atomic nucleus. The behavior of the wave functions of an incoming electron with a given asymptotic momentum in the nuclear region is discussed in detail and the results are compared to different approximations used in the data analysis for quasielastic electron scattering off medium and highly charged nuclei. It is found that most of the approximations provide an accurate description of the electron wave functions in the range of electron energies above 100 MeV typically used in experiments for quasielastic electron scattering off nuclei only near the center of the nucleus. It is therefore necessary that the properties of exact wave functions are investigated in detail in order to obtain reliable results in the data analysis of quasielastic (e, e ′ p) knockout reactions or inclusive quasielastic (e, e ′ ) scattering. Detailed arguments are given that the effective momentum approximation with a fitted potential parameter is a viable method for a simplified treatment of Coulomb corrections for certain kinematical regions used in experiments. Numerical calculations performed within the framework of the single particle shell model for nucleons lead to the conclusion that our results are incompatible with calculations performed about a decade ago, where exact electron wave functions were used in order to calculate Coulomb corrections in distorted wave Born approximation. A discussion of the exact solutions of the Dirac equation for free electrons in a Coulomb field generated by a point-like charge and some details relevant for the numerical calculations are given in the appendix.

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“…Some particulary transparent results have been obtained using the eikonal approximation to derive an effective-momentum approximation (ema) [22,23] that produces results very similar to plane-wave results. It is important to include focusing factors such as those found in the WKB approximation [24] and revisited more recently in quasi-elastic scattering [26,27]. However, the attempts to combine the eikonal analysis with focusing factors suffer from the lack of a systematic basis.…”

Section: Introductionmentioning

confidence: 99%

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

Tjon

Wallace

2009

Indian J Phys

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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.

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Coulomb corrections for quasielastic scattering: eikonal approximation

Cited by 12 publications

References 34 publications

Precise Measurement of the Nuclear Dependence of Structure Functions in Light Nuclei

Precise Measurement of the Nuclear Dependence of Structure Functions in Light Nuclei

Coulomb distortion of relativistic electrons in the nuclear electrostatic field

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

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