Elastic electron-deuteron scattering at high energy

Relativistic formulas for the deuteron electromagnetic form factors are calculated in the impulse approximation retaining terms to all orders in $\frac{Q^2}{M^2}\cong {\left(\frac{v}{c}\right)}^2$. The formulas are given as double integrals over the deuteron wave functions in momentum space, and hence can be evaluated for any deuteron model. We evaluate these formulas numerically for 9 different deuteron models: Reid soft core, two Lomon-Feshbach models, three Holinde-Machleidt models, and three four-component relativistic models. All of the models give results for the $A$ structure function considerably below the experimental results; the effect of the relativistic treatment is to reduce the size of $A$ by a factor of 2 to 5 at $Q^2$ of 100 ${\mathrm{fm}}^{-2\mathrm{}}$ over what it would be in the nonrelativistic approximation. We discuss briefly the role of exchange currents; the pair terms are included in our calculation in a completely consistent manner, but the explicit $\rho \pi \gamma$ contributions need to be calculated relativistically. We discuss in some detail the sensitivity of our calculation to the almost unknown neutron electric form factor, observing that a $G_{\mathrm{En}}$ roughly twice $G_{\mathrm{Ep}}$ in the region of $Q^2=100\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$ would enable us to fit the data even without any $\rho \pi \gamma$ contributions. We discuss the high $Q^2$ limits of our formulas, obtaining the result that the form factor falls one power of $Q^2$ faster than that predicted by the dimensional-scaling-quark model. We also study the low $Q^2$ limits and give explicit formulas for the corrections to the deuteron magnetic and quadrupole moments.