Deuteron Electromagnetic Form Factors Research Articles

Polarization Effects in Elastic Electron-Deuteron Scattering

A relativistic calculation is made of the effects of polarization in elastic electron-deuteron scattering in order to provide a theoretical basis for the complete measurement of the deuteron electromagnetic form factors. The $S$ matrix is calculated in the first Born approximation using the helicity representation for the incoming and outgoing particle states. The density matrix for the final state is obtained for an arbitrary initial state in the deuteron spin space. The two polarization experiments most likely to be feasible in the near future are examined in detail. These are (i) measurement of the spin alignment of the recoil deuteron for scattering of unpolarized electrons on unpolarized deuterons; and (ii) measurement of the differential cross section for scattering of unpolarized electrons on polarized deuterons. In particular, it is found that the interference term between the deuteron charge and quadrupole-moment form factors can lead to a measurable effect of 10-15% for a "reasonable" deuteron tensor polarization analyzer, or for a polarized deuteron target with percentage tensor polarization greater than about 0.1. These experiments provide a method for the separation of the deuteron charge and electric quadrupole form factors. Measurement of the latter provides a sensitive test of the $D$-state structure of the deuteron.

Relativistic Calculation of the Deuteron Electromagnetic Form Factor. I

The foundations of a relativistic theory of the deuteron-electromagnetic form factor are discussed. The theory is based on single-variable unsubtracted dispersion relations and coupled unitarity equations. Because of the presence of very low anomalous thresholds, only a few diagrams need be considered to give a satisfactory low-momentum transfer theory, and the diagrams with thresholds below 36${\mathrm{\ensuremath{\mu}}}^{2}$ are tabulated. The scalar theory for a subset of these diagrams (corresponding to a one-pion-exchange approximation) is examined and found to be in close correspondence with potential theory. Special attention is given to the anomalous thresholds. The role of the 3-pion state is discussed. Numerical calculations are reserved for future papers.

Nucleon-Nucleon Triplet-Even Potentials

We have found a number of triplet-even potentials that fit the deuteron data, and yield scattering lengths falling within the rather large range of uncertainty of this quantity. The potentials behave at a large distance such as the one-pion exchange potential as required by meson theory. Potentials which fit the deuteron data and obey this asymptotic requirement can make a fairly unique prediction for the deuteron $D$-state probability if the triplet scattering length is accurately known. The phase shifts for our potentials have been calculated at 95, 210, and 310 Mev, and they fall within the range presently allowed by phase-shift analysis of the $n\ensuremath{-}p$ data. The deuteron electromagnetic form factor was computed for some of the potentials, and the scalar nucleon form factor ${{F}_{1}}^{n}+{{F}_{1}}^{p}$ and neutron form factor ${{F}_{1}}^{n}$ deduced from elastic electron-deuteron scattering data in the momentum transfer range $ql~3$ ${\mathrm{f}}^{\ensuremath{-}1}$. This deduction depends, to a high degree of accuracy, only on the well-established one-pion exchange potential tail of the potential, and not on the inner region. We find that ${{F}_{1}}^{n}$ is zero, or very small and negative.

Inelastic Electron-Deuteron Scattering Cross Sections at High Energies. II. Final-State Interactions and Relativistic Corrections

Measurements of the cross-section $\frac{{d}^{2}\ensuremath{\sigma}}{(d{\ensuremath{\Omega}}_{e}d{{E}_{e}}^{\ensuremath{'}})}$ for the inelastic electron-deuteron scattering process $e+d\ensuremath{\rightarrow}e+n+p$ have been used to determine the electromagnetic structure of the neutron. The effects on the theoretical cross section of interactions between the outgoing nucleons are examined in detail using the methods of a previous paper. The transition matrix elements connecting the initial state of the two-nucleon system (the deuteron) to a final state with specified total, orbital, and spin angular momenta are calculated using approximate wave functions which are matched to the experimentally determined neutron-proton scattering phase shifts. While individual matrix elements may be drastically changed by the distortion of the final-state wave functions by the neutron-proton interaction, the over-all corrections to the peak value of the cross section are found to be small (-1 to -2%) for electron momentum transfers in the range $q=3.4\ensuremath{-}2.6$ ${\mathrm{f}}^{\ensuremath{-}1}$. The precise magnitude of the corrections is somewhat uncertain because of the approximate nature of the wave functions, but it unlikely either that they are large, or that the corrections could become positive. The effects of final-state interactions on the cross-section $\frac{{d}^{2}\ensuremath{\sigma}}{(d{\ensuremath{\Omega}}_{e}d{{E}_{e}}^{\ensuremath{'}})}$ are also examined for final electron energies near the upper limit of the inelastic continuum. In this region, the nucleons emerge with low relative momenta, and, in agreement of the predictions of Jankus, the cross section is found to be drastically changed by the strong interactions in the final $S$ states. However, it is shown that the presence in the neutron-proton interaction of a strongly repulsive core results in a considerable diminution of the cross section relative to the predictions of Jankus for large values of $q$. This lowering of the cross section has been observed by Kendall et al. Results obtained with approximate repulsive core wave functions provide a reasonable fit both to the inelastic cross section near the end point, and to the deuteron electromagnetic form factor obtained from elastic electron-deuteron scattering. Finally, the relativistic theory of inelastic electron-deuteron scattering is examined using the methods of dispersion relations. It is found that in the region of the large peak, the cross-section $\frac{{d}^{2}\ensuremath{\sigma}}{(d{\ensuremath{\Omega}}_{e}d{{E}_{e}}^{\ensuremath{'}})}$ is given essentially correctly by a nonrelativistic calculation using a modified Hamiltonian, provided the results are interpreted correctly with respect to the kinematics. The approximations inherent in the calculation are examined in detail. The resulting cross section differs significantly from the modified Jankus cross section which has been used in the analysis of the high-energy electron-deuteron scattering data obtained by the Stanford group. It is found that the apparent values of the neutron charge form factor ${F}_{1n}$ are reduced essentially to zero for ${q}^{2}$ in the range $5 {\mathrm{f}}^{\ensuremath{-}2}\ensuremath{\le}{q}^{2}\ensuremath{\le}20 {\mathrm{f}}^{\ensuremath{-}2}$ when relativistic corrections, the effects of the deuteron $D$-states cattering, and the effects of final-state interactions are taken into account. Corresponding reductions in the value of the neutron anomalous magnetic moment form factor ${F}_{2n}$ range up to about 30%, and bring ${F}_{2n}$ into closer agreement with ${F}_{2p}$. A complete re-analysis of the experimental data will be necessary.