Meson exchange currents in electromagnetic one-nucleon emission

Giusti, C.; Pacati, F.D.

doi:10.1103/physrevc.67.044601

Cited by 16 publications

(49 citation statements)

References 60 publications

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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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Section: Introductionmentioning

confidence: 99%

Coulomb distortion of relativistic electrons in the nuclear electrostatic field

2005

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“…The eikonal method and its higher approximations, which can be obtained from an iterative procedure, is expected to lead to an asymptotic, rather than a convergent expansion [9]. Therefore, its use for the calculation of exclusive cross sections may be problematic according to Giusti and Pacati [10,11], but the good agreement for the inclusive cross section with the exact calculations by Kim et al seems to justify the method in this case. Additionally, the eikonal approximation used in [10,11] is not equivalent to the approach used in this paper, since we do not calculate the electron wave phase shift from an expansion around the center of the nucleus.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, its use for the calculation of exclusive cross sections may be problematic according to Giusti and Pacati [10,11], but the good agreement for the inclusive cross section with the exact calculations by Kim et al seems to justify the method in this case. Additionally, the eikonal approximation used in [10,11] is not equivalent to the approach used in this paper, since we do not calculate the electron wave phase shift from an expansion around the center of the nucleus. For exclusive cross sections, not only exact wave functions for the electrons are needed, but also an accurate description of the proton or neutron wave functions.…”

Section: Introductionmentioning

confidence: 99%

Coulomb corrections for quasielastic scattering: eikonal approximation

Aste¹,

Hencken²,

Jourdan³

et al. 2004

Nuclear Physics A

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We address the problem of including Coulomb distortion effects in inclusive quasielastic (e, e ′ ) reactions using the eikonal approximation. Our results indicate that Coulomb corrections may become large for heavy nuclei for certain kinematical regions. The issues of our model are presented in detail and the results are compared to calculations of the Ohio group, where Dirac wave functions were used both for electrons and nucleons. Our results are in good agreement with those obtained by exact calculations.

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“…As a consequence, various approximate methods have been proposed in the past for the treatment of Coulomb distortions [7,8,9,10,11,12,13,14,15], and there is an extensive literature on the so-called eikonal approximation [16,17,18,19,20,21,22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

Aste

Trautmann

2007

Eur. Phys. J. A

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The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasielastic (e, e ′ ) scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial and final state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e, e ′ ) scattering off heavy nuclei for sufficiently high electron energies and momentum transfer.

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Meson exchange currents in electromagnetic one-nucleon emission

Cited by 16 publications

References 60 publications

Coulomb distortion of relativistic electrons in the nuclear electrostatic field

Coulomb distortion of relativistic electrons in the nuclear electrostatic field

Coulomb corrections for quasielastic scattering: eikonal approximation

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

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