Coulomb distortion of relativistic electrons in the nuclear electrostatic field

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.

arXiv comment21 pages, 5 figures, LATEX, one new section and some references added

References in corpus (7)

• Spectroscopic Factors in ${}^{40}$Ca and ${}^{208}$Pb from $(e,e^{\prime }p)$: Fully Relativistic Analysis
• Approximate treatment of electron Coulomb distortion in quasielastic (e,e') reactions
• Is the Coulomb sum rule violated in nuclei?
• Improved effective momentum approximation for quasielastic (e,e') scattering off highly charged nuclei
• Coulomb Distortion in Quasielastic $(e,e^{\prime })$ Scattering on Nuclei: Effective Momentum Approximation and Beyond
• Coulomb corrections for quasielastic (e,e') scattering: eikonal approximation
• Coulomb Corrections for Coherent Electroproduction of Vector Mesons: Eikonal Approximation

Cited by in corpus (29)

• Nucleon-Nucleon Correlations, Short-lived Excitations, and the Quarks Within
• Inclusive quasi-elastic electron-nucleus scattering
• New measurements of the EMC effect in very light nuclei
• New measurements of high-momentum nucleons and short-range structures in nuclei
• EMC and Polarized EMC Effects in Nuclei
• Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random phase approximation
• A detailed study of the nuclear dependence of the EMC effect and short-range correlations
• First Measurement of the Ti$(e,e^{\prime })\mathrm{X}$ Cross Section at Jefferson Lab
• First Measurement of the Ar$(e,e^{\prime })X$ Cross Section at Jefferson Lab
• Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule
• Scaling of the F_2 structure function in nuclei and quark distributions at x>1
• Determination of the argon spectral function from (e,e'p) data
• Measurement of charged-pion production in deep-inelastic scattering off nuclei with the CLAS detector
• Measurement of transparency ratios for protons from short-range correlated pairs
• Measurement of the cross sections for inclusive electron scattering in the E12-14-012 experiment at Jefferson Lab
• Coulomb sum rule in quasielastic region
• Measurement of Nuclear Transparency Ratios for Protons and Neutrons
• Nuclear-level Effective Theory of $\mu \to e$ Conversion: Formalism and Applications
• Search for three-nucleon short-range correlations in light nuclei
• Measurement of the Ar(e,e${}^{\prime }$ p) and Ti(e,e${}^{\prime }$ p) cross sections in Jefferson Lab Hall A
• Determination of the titanium spectral function from (e,e'p) data
• Neutrino-nucleus cross sections in ${}^{12}C$ and ${}^{40}Ar$ with KDAR neutrinos
• Measurement of the Beam-Normal Single-Spin Asymmetry for Elastic Electron Scattering from ${}^{12}$C and ${}^{27}$Al
• New Measurements of the EMC Effect in Few-Body Nuclei
• Coulomb distortion effects in quasi-elastic (e,e') scattering on heavy nuclei
• Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation
• Dispersive Corrections to the Born Approximation in Elastic Electron-Nucleus Scattering in the Intermediate Energy Regime
• Parity-Violating Inelastic Electron-Proton Scattering at Low $Q^2$ Above the Resonance Region
• Investigation of Medium Modifications to ${}^{12}$C Structure Functions in the Resonance Region