Elastic electron-deuteron scattering beyond one-photon exchange

Abstract

We discuss elastic ed scattering beyond the Born approximation. The reaction amplitude contains six generalized form factors, but only three linearly independent combinations of them (generalized charge, quadrupole and magnetic form factors) contribute to the reaction cross section in second order perturbation theory. We examine the two-photon exchange and find that it includes two types of diagrams, where two virtual photons are interacting with the same nucleon and where the photons are interacting with different nucleons. It is shown that the two-photon exchange amplitude is strongly connected with the deuteron wave function at short distances.PACS numbers: 13.40. Gp,21.45.Bc,25.30.Bf I. INTRODUCTIONThe study of electron scattering on the nucleon and the light nuclei provides a convenient tool to study the structure of strongly interacting systems. Due to the smallness of the fine structure constant α ≈ 1 137 , one may expect that the Born approximation (one-photon exchange, OPE) should describe such processes with an accuracy of a few percent. Nevertheless, JLab polarization measurements of G p, together with their theoretical analysis [4-7], show that higher order perturbative effects, such as two-photon exchange (TPE), can strongly affect some observables of the elastic electron-nucleon scattering.Also for more complicated hadronic systems, like the deuteron, 3 He, 4 He, etc., TPE should contribute. Thus for precise studies of these nuclei a quantitative theoretical investigation of TPE effects is important; until now only a few estimates have been done of the contribution of TPE [8][9][10][11][12][13].The aim of this paper is to estimate the TPE amplitude for ed-scattering in the framework of semi-relativistic calculations, with deuteron wave functions from "realistic" NN potentials.The paper is organized as follows. In Sect. II we study the general structure of the reaction amplitude beyond OPE and define six independent generalized form factors which determine the amplitude. We show that only three linearly independent combinations of these generalized form factors contribute to the cross section in second order perturbation theory. We call the corresponding combinations of the form factors generalized charge, quadrupole and magnetic form factors. These generalized form factors are computed in Sect. III. Sect. IV contains numerical results and a brief discussion. II. KINEMATICS AND DEFINITIONSThe electron and deuteron momenta in the initial and final states of elastic ed scattering are denoted by k, k ′ and d, d ′ , respectively; q = k − k ′ is the transferred momentum; M and m are deuteron and nucleon masses; actual calculations will be done with m ≈ 1 2 M . All calculations are done in the Breit frame, where the deuteron has the same energy E d in the initial and final * Electronic address: kobushkin@bitp.kiev.ua

Nucleon Momentum Distributions in ³He and Three-Body Interactions

“…The results of calculations published in Ref. [23] and based on the GlauberSitenko model support the interpretation of this enhancement in the momentum distribution of protons in a deuteron as a manifestation of the Coulomb interaction. Of course, the final state interaction also might be significant in the region of small k. In case of the deuteron breakup, this effect was (in part, at least) taken into account in Ref.…”

“…Of course, the final state interaction also might be significant in the region of small k. In case of the deuteron breakup, this effect was (in part, at least) taken into account in Ref. [23].…”

Two-photon exchange and elastic scattering of longitudinally polarized electrons on polarized deuterons

“…[5] with the deuteron wave function from CD-Bonn [11] and Paris [12] NN potentials. The deuteron form factors G C (Q 2 ), G Q (Q 2 ), and G M (Q 2 ) are taken from the parametrization of Ref.…”

“…Similarly to elastic electron-nucleon scattering, two-photon exchange (TPE) is one of the most important effects beyond the Born approximation in elastic ed scattering [2][3][4][5].…”

“…Both types of diagrams were calculated simultaneously in Ref. [5] within a semirelativistic approximation, with deuteron wave functions from "realistic" nucleon-nucleon (NN) potentials.…”