J. W. Van Orden

Mesonic processes in deep-inelastic electron scattering from nuclei☆

Abstract Inelastic electron scattering is considered in the energy and momentum transfer region associated with the quasielastic and 3-3 resonance pion electroproduction peaks. Calculations of two-nucleon ejection via two-body meson-exchange currents (MEC) and of pion electroproduction from threshold through the 3-3 resonance are presented using the Fermi gas model of the nucleus. The MEC contribution is found to be significant in this region, and helps to account for the discrepancy between theory and experiment in the “dip” between the quasielastic and 3-3 resonance peaks.

The Deuteron: Structure and Form Factors

Diplon, deuton, deuteron: under different names, the nucleus of deuterium, or diplogen, has been the subject of intense studies since its discovery in 1932. As the only two-nucleon bound state, its properties have continuously been viewed as important in nuclear theory as the hydrogen atom is in atomic theory. Yet, ambiguities remain in the relativistic description of this system and the two-nucleon picture is incomplete: meson exchange and nucleon excitation into resonances should be considered in the deuteron description. The question of rare configurations where the two nucleons overlap and loose their identity is still under debate. We are still looking for the elusive effects of quarks in the nuclear structure.

Meson exchange currents in deep inelastic electron scattering from nuclei

Abstract The contributions to the electron scattering cross section arising from two-nucleon emission via meson exchange current interactions is calculated in the Fermi gas model. Sizeable effects are found at large energy transfers and lead to a partial filling of the “dip” between the quasielastic peak and the analogous peak associated with the excitation of the 3-3 resonance.

Quark hadron duality in a relativistic, confining model

Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regimes. While duality is well established experimentally, our current theoretical understanding is still incomplete. We employ a simple model to qualitatively reproduce all the features of Bloom-Gilman duality as seen in electron scattering. In particular, we address the role of relativity, give an explicit analytic proof of the equality of the hadronic and partonic scaling curves, and show how the transition from coherent to incoherent scattering takes place.

Electromagnetic Structure of Few-Nucleon Ground States

Experimental form factors of the hydrogen and helium isotopes, extracted from an up-to-date global analysis of cross sections and polarization observables measured in elastic electron scattering from these systems, are compared to predictions obtained in three different theoretical approaches: the first is based on realistic interactions and currents, including relativistic corrections (labeled as the conventional approach); the second relies on a chiral effective field theory description of the strong and electromagnetic interactions in nuclei (labeled χEFT); the third utilizes a fully relativistic treatment of nuclear dynamics as implemented in the covariant spectator theory (labeled CST). For momentum transfers below fm−1 there is satisfactory agreement between experimental data and theoretical results in all three approaches. However, at fm−1, particularly in the case of the deuteron, a relativistic treatment of the dynamics, as is done in the CST, is necessary. The experimental data on the deuteron A structure function extend to fm−1, and the close agreement between these data and the CST results suggests that, even in this extreme kinematical regime, the study of few-body form factors provides no evidence for new effects coming from quark and gluon degrees of freedom at short distances.

Models for relativistic coulomb sum rules: Expansions in moments of the nuclear momentum density

Abstract Relativistic Coulomb sum rules for quasielastic electron scattering from nuclei are developed using a class of relativistic models for the nuclear ground-state momentum distribution. Approximate sum rules at constant 3- or 4-momentum transfer are expressed as expansions in moments of the momentum distribution. New sum-rule functions are derived which, even for very large values of energy and momentum where relativistic effects become dominant, approach simple asymptotic values; in doing so they approximately retain the flavor of the nonrelativistic Coulomb sum rule which approaches Z . Specific ways of achieving an optimum separation of effects relating to the electromagnetic response of a single nucleon and of a many-body system of structureless particles are discussed, including a study of sensitivities to alternative parameterizations of G En . Comparisons of results using different momentum distributions for the case of 16 O are presented.

Modeling quark-hadron duality for relativistic, confined fermions

We discuss a model for the study of quark-hadron duality in inclusive electron scattering based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss similarities and differences to previous models that simplified the situation by treating either the quarks or all particles as scalars. We discuss the scaling results for PWIA and FSI, and the approach to scaling using the analog of the Callan-Gross relation for y-scaling.

Normalization of the covariant three-body bound state vertex function

The normalization condition for the relativistic three nucleon Bethe-Salpeter and Gross bound state vertex functions is derived, for the first time, directly from the three body wave equations. It is also shown that the relativistic normalization condition for the two body Gross bound state vertex function is identical to the requirement that the bound state charge be conserved, proving that charge is automatically conserved by this equation.

Electromagnetic interactions for the two-body spectator equations

This paper presents a new non-associative algebra which is used to (1) show how the spectator (or Gross) two-body equations and electromagnetic currents can be formally derived from the Bethe-Salpeter equation and currents if both are treated to all orders, (2) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (3) prove that the currents so derived are exactly gauge invariant when truncated consistently to any finite order. In addition to presenting these new results, this work complements and extends previous treatments based largely on the analysis of sums of Feynman diagrams.

Origin of relativistic effects in the reaction D (e, e-prime p) n at GeV energies

In a series of recent publications, a new approach to the non-relativistic reduction of the electromagnetic current operator in calculations of electro-nuclear reactions has been introduced. In one of these papers, the conjecture that at energies of a few GeV, the bulk of the relativistic effects comes from the current and not from the nuclear dynamics was made, based on the large relativistic effects in the transverse-longitudinal response. Here, the authors explicitly compare a fully relativistic, manifestly covariant calculation performed with the Gross equation, with a calculation that uses a non-relativistic wave function and a fully relativistic current operator. They find very good agreement up to missing momenta of 400 MeV/c, thus confirming the previous conjecture. They discuss slight deviations in cross sections for higher missing momenta and their possible origin, namely p-wave contributions and off-shell effects.