Fermi-motion corrections for deuterium targets

A covariant analysis is given of the smearing effects of the Fermi motion of the nucleons in a deuterium target, in the impulse approximation. It is concluded that when the nucleon cross sections ${\ensuremath{\sigma}}_{p}$ and ${\ensuremath{\sigma}}_{n}$ are constant, the smearing correction vanishes: ${\ensuremath{\sigma}}_{d}={\ensuremath{\sigma}}_{p}+{\ensuremath{\sigma}}_{n}$. More generally, in a relativistic theory the correction may be expanded in powers of ${(\frac{\ensuremath{\epsilon}}{M})}^{\frac{1}{2}}$, where $\ensuremath{\epsilon}$ and $M$ are the binding energy and the mass of the deuteron. However, present knowledge of the structure of the deuteron does not allow an evaluation of the coefficients in this expansion, so that the very sizable correction necessary in, for example, deep-inelastic lepton scattering on deuterium cannot be reliably determined. To rectify this situation, we urge a study of the momentum distribution of the spectator nucleon in hadronic reactions with a deuteron beam, or with a deuteron storage ring.