arXiv subjects

Franz Gross

Publications and source records attributed to Franz Gross.

66 records · Page 4Linked to original sources

arXiv1998

Pole Term and Gauge Invariance in Deep Inelastic Scattering

In this paper we reconcile two contradictory statements about deep inelastic scattering (DIS) in manifestly covariant theories: (i) the scattering must be gauge invariant, even in the deep inelastic limit, and (ii) the pole term (which is not gauge invariant in a covariant theory) dominates the scattering amplitude in the deep inelastic limit. An ``intermediate'' answer is found to be true. We show that, at all energies, the gauge dependent part of the pole term cancels the gauge dependent part of the rescattering term, so that both the pole and rescattering terms can be separately redefined in a gauge invariant fashion. The resulting, redefined pole term is then shown to dominate the scattering in the deep inelastic limit. Details are worked out for a simple example in 1+1 dimensions.

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arXiv1998

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.

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arXiv1997

Sensitivity of the deuteron form factor to nucleon resonances

The sensitivity of the deuteron form factor to contributions from the excited states of the nucleon is explored using a simple model of the nucleon-nucleon interaction which employs a tower of charged nucleon resonances. The model is manifestly covariant, analytically solvable, and gauge invariant. The consequences of this model are studied in the simplest possible framework. We assume that all particles have spin zero and that the tower has only three charged members, which consist of the proton, the Roper, and a higher state in the vicinity of the $D_{13}$. Nucleon-nucleon S-wave phase shifts and the deuteron form factor are calculated using this three member tower, and the results are compared to similar calculations using the proton ground state only. We conclude that the deuteron form factor is insensitive to the presence of excited states of the proton unless those states are of sufficiently low mass to produce strong inelasticities in $NN$ scattering channels.

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arXiv1997

Electromagnetic interactions for the two-body spectator equations

This paper presents a new non-associative algebra which is used to (i) 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, (ii) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (iii) 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.

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arXiv1997

Lagrangian with off-shell vertices and field redefinitions

Meson exchange diagrams following from a lagrangian with off-shell meson-nucleon couplings are compared with those generated from conventional dynamics. The off-shell interactions can be transformed away with the help of a nucleon field redefinition. Contributions to to the $NN$- and $3N$-potentials and nonminimal contact e.m. meson-exchange currents are discussed, mostly for an important case of scalar meson exchange. (pacs 11.10.Lm, 13.75.Cs, 21.30.-x, 24.10.Jv)

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arXiv1997

Covariant equations for the three-body bound state

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including the Wigner rotations and rho-spin decomposition of the off-shell particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative rho-spin states of the off-shell particle.

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arXiv1997

Effects of Relativistic Dynamics in $pp \to pp π^0$ near Threshold

The cross-section for threshold $π^0$ production in proton-proton collisions is evaluated in the framework of the covariant spectator description. The negative energy intermediate states are included non-perturbatively and seen to yield a considerably smaller contribution, when compared to perturbative treatments. A family of OBE-models with different off-shell scalar coupling is considered.

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arXiv1996

Relativistic calculation of the triton binding energy and its implications

First results for the triton binding energy obtained from the relativistic spectator or Gross equation are reported. The Dirac structure of the nucleons is taken into account. Numerical results are presented for a family of realistic OBE models with off-shell scalar couplings. It is shown that these off-shell couplings improve both the fits to the two-body data and the predictions for the binding energy.

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arXiv1996

Two-pion exchange potential and the $πN$ amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $πN$ scattering amplitude which includes $Δ$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $πN$ amplitude satisfies chiral symmetry constraints and fits $πN$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.

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arXiv1995

A Comment on General Formulae for Polarization Observables in Deuteron Electrodisintegration and Linear Relations

We establish a simple, explicit relation between the formalisms employed in the treatments of polarization observables in deuteron two-body electrodisintegration published by Arenhövel, Leidemann, and Tomusiak in Few-Body Systems {\bf 15}, 109 (1993) and the results of the present authors published in Phys.~Rev.~C {\bf 40}, 2479 (1989). We comment on the overlap between the two sets of results.

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arXiv1995

Extraction of the Ratio of the Neutron to Proton Structure Functions from Deep Inelastic Scattering

We study the nuclear ($A$) dependence of the European Muon Collaboration (EMC) effect at high values of $x$ ($x \geq 0.6$). Our approach makes use of conventional nuclear degrees of freedom within the Relativistic Impulse Approximation. By performing a non-relativistic series expansion we demonstrate that relativistic corrections make a substantial contribution to the effect at $x \gtrsim 0.6$ and show that the ratio of neutron to proton structure functions extracted from a global fit to all nuclei is not inconsistent with values obtained from the deuteron.

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arXiv1994

Low energy theorem for scalar and vector interactions of a composite spin-1/2 system

Scalar and vector interactions, with the scalar interaction coupled to a composite spin-1/2 system so as to cause a shift of its mass, are shown to obey a low-energy theorem which guarantees that the second order interaction due to z-graphs is the same as for a point Dirac particle. Off-shell and contact interactions appropriate to the composite system cancel and this is verified in a model of a composite fermion. The result provides a justification for the use of the Dirac equation as it has been in relativistic nuclear scattering and mean field theories.

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