dorsal/arxiv
View SchemaCoulomb distortion of relativistic electrons in the nuclear electrostatic field
| Authors | Andreas Aste, Cyrill von Arx, Dirk Trautmann |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0502074 |
| URL | https://arxiv.org/abs/nucl-th/0502074 |
| DOI | 10.1140/epja/i2005-10169-0 |
| Journal | Eur.Phys.J. A26 (2005) 167-178 |
Abstract
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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"abstract": "Continuum states of the Dirac equation are calculated numerically for the\nelectrostatic field generated by the charge distribution of an atomic nucleus.\nThe behavior of the wave functions of an incoming electron with a given\nasymptotic momentum in the nuclear region is discussed in detail and the\nresults are compared to different approximations used in the data analysis for\nquasielastic electron scattering off medium and highly charged nuclei. It is\nfound that most of the approximations provide an accurate description of the\nelectron wave functions in the range of electron energies above 100 MeV\ntypically used in experiments for quasielastic electron scattering off nuclei\nonly near the center of the nucleus. It is therefore necessary that the\nproperties of exact wave functions are investigated in detail in order to\nobtain reliable results in the data analysis of quasielastic (e,e\u0027p) knockout\nreactions or inclusive quasielastic (e,e\u0027) scattering. Detailed arguments are\ngiven that the effective momentum approximation with a fitted potential\nparameter is a viable method for a simplified treatment of Coulomb corrections\nfor certain kinematical regions used in experiments. Numerical calculations\nperformed within the framework of the single particle shell model for nucleons\nlead to the conclusion that our results are incompatible with calculations\nperformed about a decade ago, where exact electron wave functions were used in\norder to calculate Coulomb corrections in distorted wave Born approximation. A\ndiscussion of the exact solutions of the Dirac equation for free electrons in a\nCoulomb field generated by a point-like charge and some details relevant for\nthe numerical calculations are given in the appendix.",
"arxiv_id": "nucl-th/0502074",
"authors": [
"Andreas Aste",
"Cyrill von Arx",
"Dirk Trautmann"
],
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"doi": "10.1140/epja/i2005-10169-0",
"journal_ref": "Eur.Phys.J. A26 (2005) 167-178",
"title": "Coulomb distortion of relativistic electrons in the nuclear electrostatic field",
"url": "https://arxiv.org/abs/nucl-th/0502074"
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