Polarization Effects in Elastic Electron-Deuteron Scattering

Abstract

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.