Electron-deuteron tensor polarization and the two-nucleon force

Abstract

Electron-deuteron scattering observables, including the tensor polarizations ${T}_{20}$, ${T}_{2\ifmmode\pm\else\textpm\fi{}1}$, ${T}_{2\ifmmode\pm\else\textpm\fi{}2}$, are calculated for a variety of $N\ensuremath{-}N$ potential models. The main goal is to determine how the tensor polarization experiments can help distinguish competing potential models with respect to off-shell behavior and tensor force strength. The pair meson-exchange-current correction of Gari and Hyuga is included in the analysis as well as a correction suggested by Friar for energy-dependent potentials. It is found that whereas electron-deuteron elastic scattering cross sections do not readily distinguish different potentials, the tensor polarizations do. The tensor polarization ${T}_{20}$ mainly distinguishes potentials with different deuteron $s$-wave momentum distributions, but does not distinguish potentials with different $d$-state probabilities (${P}_{D}$). The tensor polarization ${T}_{2\ifmmode\pm\else\textpm\fi{}1}$, since it factors essentially into a product of the magnetic and quadrupole form factors, allows for the extraction of the quadrupole form factor which is closely related to the tensor force strength and ${P}_{D}$. The tensor polarization ${T}_{2\ifmmode\pm\else\textpm\fi{}2}$ is completely determined by the elastic scattering cross sections and magnetic form factor, and yields no additional information on the $N\ensuremath{-}N$ force unobtainable from elastic scattering measurements. The tensor polarizations ${T}_{20}$ and ${T}_{21}$ have maximum values of order unity in the region $q=2 \mathrm{to} 5$ ${\mathrm{fm}}^{\ensuremath{-}1}$. The calculations indicate that measurements of ${T}_{20}$ for $2\ensuremath{\lesssim}q\ensuremath{\lesssim}5$ ${\mathrm{fm}}^{\ensuremath{-}1}$, and ${T}_{2\ifmmode\pm\else\textpm\fi{}1}$ for $3\ensuremath{\lesssim}q\ensuremath{\lesssim}5$ ${\mathrm{fm}}^{\ensuremath{-}1}$ could yield important information on the off-shell behavior and tensor force strength. The meson-exchange-current and energy-dependence corrections are important and must be taken into account to extract potential properties from such experiments.NUCLEAR STRUCTURE $^{2}\mathrm{H}$: form factors, tensor polarization calculated: dependence on off-shell behavior and ${P}_{D}$; seven potential models; pair currents included.