Relativistic Corrections to the Impulse Approximation in Elastic Electron-Deuteron Scattering

Equations are derived for the deuteron form factor in the impulse approximation which include corrections to order $M^{-2\mathrm{}}$, where $M$ is the nucleon mass. The corrections are of two types, arising from (1) the expansion of the nucleon current to order $M^{-2\mathrm{}}$ and (2) the treatment of the deuteron wave function in a relativistic manner so as to retain terms of order $M^{-2\mathrm{}}$ which describe the distortion of the wave function of a moving deuteron. While some of the former corrections have been discussed by several people, detailed results for the latter corrections have not been given before. All of the results are expressed as functionals of the non-relativistic $S$- and $D$-state wave functions, so that numerical results may be calculated for any deuteron model. Numerical estimates of the charge correction term indicate that it is large enough to substantially affect the determination of the neutron-charge form factor from this experiment, making the form factor more positive than results obtained from the uncorrected theory. Corrections to the magnetic moment are also discussed.