Modern Topics in Electron Scattering

The following sections are included:

• FOREWORD

• CONTENTS

Understanding the underlying quark and gluon structure of the nucleons is not only a fundamental objective in its own tight, but also an essential first step in providing a basis within QCD for nuclear physics. In this article I present a pedagogical introduction to a simple but very successful nonrelativistic constituent quark model for baryons.

The following sections are included:

• Introduction

• Electroproduction on a free nucleon

• Nuclear Δ-excitation and -propagation in the Δ - hole approach

• Inclusive electron - nucleus cross scattering

• Summary and Conclusions

• Acknowledgements

• References

We review some of the basics in inclusive electron scattering processes and discuss the possible effects of nucleon modifications. The concept of modified nucleons is only useful when within the impulse approximation a satisfactory description of experimental data can be obtained. Furthermore the concept should be applicable independent of the processes under consideration. We discuss in detail the impulse approximation or convolution picture, which can be used in quasi-elastic electron-nucleus scattering or in deep inelastic scattering.

The physics program and the requirements for large acceptance detectors in electromagnetic nuclear physics are discussed. As a specific example, the CEBAF Large Acceptance Spectrometer is presented.

An introduction to the theory of three-nucleon systems is given, with an emphasis on basic principles. The physical processes which complicate the specification of boundary conditions are discussed, and the Faddeev equations motivated. The latter are discussed in configuration space. Results of converged calculations with realistic potentials are compared with experimental data.

The role of subnuclear degrees of freedom in terms of meson and isobar degrees of freedom is discussed for the simplest process in nuclear physics, i.e., the electromagnetic break-up of the deuteron. The various theoretical schemes for incorporating such degrees of freedom either explicitely or as effective operators are briefly reviewed. The principle of minimal substitution as a means to construct effective two-body exchange current operators is illustrated and explicit expressions for pion exchange are given. The cross sections for photo- and electrodisintegration of the deuteron are expressed in terms of the t-matrix elements. The different theoretical methods for the calculation of the t-matrix are described and the essential ingredients for the non-relativistic evaluation including the most important relativistic corrections of lowest order are outlined. For specific experiments in photo- and electrodisintegration theoretical results are compared to experimental data and the present status of our understanding of these processes is assessed.

In this article we discuss electron-nucleus scattering in the framework of the nuclear many-body theory. Only the nucleon degrees of freedom are treated explicitly in this approach, the effects of all other degrees of freedom are implicit in the nuclear interaction and current operators. The ground state properties of light nuclei can be accurately calculated and the theoretical results are in agreement with the experimental data. However, reactions sensitive to the wave functions of continuum states are only qualitatively understood.

The following sections are included:

• Introduction and Overview
  • Deuteron Form Factors and Static Moments
  • Deuteron Photodisintegration
  • Deuteron Electrodisintegration and Radiative Neutron Capture
  • Three Nucleon Form Factors
  • Nucleon-Nucleon Interaction
  • Conclusions, Discussion, and Assessment

• Relativistic Corrections to Order (v/c)²
  • Corrections to the One Body Charge Operator
  • Nuclear Boosts - Generator Method
  • Nuclear Boost - Covariant Method
  • Interlude: Discussion and Comparison
  • Retardation Corrections
  • Pair Contributions
  • Conclusions

• Covariant Methods
  • Introduction and Comparisons
  • Current Conservation
  • Applications of the Bethe-Salpeter Equation
  • Applications of the Spectator Equation
  • Conclusions

• Acknowledgements

• References

By appropriate choice of the kinematics it has been possible to isolate and to master the various reaction mechanisms which dominate exclusive inelastic reactions induced by photons and electrons in few body systems. The nucleon momentum distribution has been determined up to 500 MeV/c : its high momentum components are due to two body correlations. Evidence for three body mechanisms has been found. Now these reactions provide us with a powerful tool with which to determine the various components of the nuclear wave functions, to study correlations between two or more nucleons and to study possible modifications of the elementary electromagnetic operators (the nucleon form factors, for instance) in the nuclear medium. The determination of the various spin observables appears to be particularly interesting.

The following sections are included:

• INTRODUCTION

• INTERACTIONS and CURRENTS
  • Nucleon-Nucleon Interaction
  • Meson-exchange currents
  • Nucleon form factors

• DEUTERON FORM FACTORS
  • The deuteron A(Q²) structure function
  • The deuteron tensor polarization t₂₀
  • The deuteron B(Q²) structure function
  • Deuteron Electrodisintegration at Threshold

• A = 3 AND A = 4 NUCLEI
  • Trinucleon Magnetic Form Factors
  • Trinucleon Charge Form Factors
  • The form factor of ⁴He

• FORM FACTORS IN ISOSPIN SPACE

• THE NEW FRONTIERS

• References

The following sections are included:

• INTRODUCTION

• CHARGE DISTRIBUTIONS
  • Mean Field Predictions
  • Experimental Determination of Charge Densities
  • Comparison of e⁺ and e⁻ Scattering
  • Experimental Uncertainty in the Nuclear Interior

• NUCLEAR POLARIZATION AND NUCLEAR COMPRESSIBILITY

• SINGLE PARTICLE DISTRIBUTIONS
  • The 3s Charge Distribution
  • Magnetization Distributions of Valence Orbits in the Pb region
  • Inelastic Transitions
  • Single Nucleon Knock-out

• SINGLE PARTICLE ORBITS AND OCCUPATION NUMBERS
  • Natural Orbits
  • Mean Field Orbits
  • Quasi-Particle Orbits
  • Occupation Probabilities

• THE SHAPE OF CORRELATED WAVE FUNCTIONS

• CONCLUSIONS

• References

Thanks to the improved characteristics of the experimental set-up electron scattering has become an excellent tool to study the structure of the nucleus. After describing globally how the nuclear structure enters in the formalism of (e,e′) reactions and how the high experimental resolution is obtained, several examples of the use of electron scattering for the study of specific nuclear structure questions are discussed.

The following sections are included:

• Introduction

• Quasifree Processes in Light Nuclei
  • The A=3 System
    • Inclusive Scattering
    • Coincidence Studies
  • A=12
    • Inclusive Scattering
    • Coincidence Studies

• Dynamical processes
  • Final State Interactions
    • Quasielastic Region
    • Dip Region
    • Δ Region
  • In-Medium Hadron Structure
  • Correlations
  • Off-Shell Form Factors and Relativistic Theories

• Summary and Concluding Remarks

• References

The electron scattering by nuclear matter is discussed in the framework of nuclear many–body theory. Microscopic calculations Of the responses and the spectral functions are reviewed. It is shown that the theoretical responses agree with the experimental data on inclusive reactions for values of the energy loss corresponding to the quasi-free peak and below. At higher energies, nuclear matter calculations reveal to be particularly useful to study final state interactions and possible time dependence of the nucleon-nucleon cross-section. The calculated nuclear matter spectral functions can explain the experimental data on the occupation probabilities and spectroscopic strengths of complex nuclei, as well as (e, e′p) cross-sections at high missing momentum.

A review is given of recent results obtained with (e,e′p) experiments in the quasi-elastic domain, which have been performed at MIT/Bates, NIKHEF and Saclay. Both the possible modifications of the electron-proton coupling in the nuclear medium and the effects of long- and short-range correlations on the proton spectra1 function are discussed.

The y-scaling property of data for inclusive electron-nucleus scattering is used to study the reaction mechanism of quasi-free scattering, bound-nucleon form factors and the nuclear spectral function. The complications due to non-nucleonic degrees of freedom and final state interaction are discussed.

The following sections are included:

• POLARIZED ELECTRONS

• PARITY-CONSERVING ELECTRON SCATTERING
  • Single-Arm Scattering from Unpolarized Targets
  • Single-Arm Scattering from Polarized Targets
  • Two-Arm Coincidence Reactions with Polarized Electrons: The Fifth Response Function
  • General Two-Arm Coincidence Reactions with Polarization Degrees of Freedom
  • A Specific Example: The Reaction

• PARITY-VIOLATING ELECTRON SCATTERING
  • Isospin Mixing in N = Z Nuclei
  • Elastic Scattering from Even-Even N ≠ Z Nuclei
  • Determination of the Neutron Charge Distribution by Scattering from the Proton
  • Strange-Quark Content of the Nucleon

• CONCLUSIONS

• REFERENCES

We present a critical review of the prospects for studying hypernuclear structure with intense CW electron beams.

We deduce basic equations of light-cone mechanics of many particle system which have correct cluster properties and Lorentz invariant on-energy-shell amplitudes. Correspondence with nonrelativistic Schrödinger equation as well as properties of the spectral function of nuclei are discussed. We explain how short range nucleon correlations in nuclei reveal itself in the high energy processes kinematically forbidden for the scattering of free nucleon. Evidence for the considerable probability of short range nucleon correlations in nuclei from high energy processes especially in lepton-nucleus processes is discussed.

A wide review is presented for the high-energy hadronic reactions problem in strong interaction physics from the early days of meson theory, Regge theory and the eightfoldway to the modern QCD period. The review is conceived as a historical guide through the literature and as a brief digest of the main theoretical methods.

The recently developed method of constructing the nuclear exchange current operators within the framework of the topological soliton (Skyrme) model is described. This approach is theoretically compact, allows treating nucleon and nuclear structure on the same footing and finally can be viewed as an effective low-energy representation of QCD. The approach also leads to some very natural connections between pionic and nuclear transition rates because the effective pion-nucleon interaction involves the isovector(exchange) current operators, Finally a discussion of the relation between exchange currents and relativistic corrections is given.

We review current ideas on the parton structure of nuclei and confront them with results of nearly ten years of experimental studies of parton distributions in nuclei using deep inelastic lepton-nucleus scattering as well as Drell-Yan processes. We find that many of the guesses about origin of the EMC effect are strongly constrained by the information about nuclear structure from other hard nuclear reactions especially high Q² nearthreshold A(e, e′) reactions. We also explain existence of a number open problems in investigations of parton distributions at x ∈ (0.001 − 2.5) in nuclei as well as in the studies of higher twist contributions to the high Q² structure functions of nuclei which are important for understanding of the structure of bound states in QCD.