Inelastic Electron-Deuteron Scattering Cross Sections at High Energies

Abstract

The effects on the cross sections for the inelastic electron-deuteron scattering process $e+d\to e+n+p$ of interactions between the outgoing nucleons are examined in detail. The cross sections are calculated in the first Born approximation with respect to the electromagnetic interaction using nucleon wave functions modified by the final state interactions. Crude estimates indicate that the peak value of the cross section $\frac{d^2\sigma }{\left(d{\Omega }_{e}d{E_e}^{\prime }\right)}$ may be decreased by ∼5-10% in the presence of such interactions. It is shown in an Appendix that additional decreases of ∼5% will result when proper account is taken of the $D$-state component of the deuteron wave function. These changes in the cross section affect appreciably the determination of the neutron magnetic form factor from the experimental scattering cross sections. A new method of measuring the magnetic form factor based on the angular distribution of the outgoing nucleons is therefore proposed which eliminates almost all the uncertainties relating to the deuteron wave function and the effects of final state interactions. This method may also be used in conjunction with the dependence of the cross sections on the electron scattering angle to study the behavior of the neutron charge form factor in the region of large momentum transfers. The polarization of the outgoing nucleons is also calculated. While significant information may in principle be obtained from polarization measurements, the required experiments do not appear to be feasible at the present time. In an Appendix, the modifications of the cross sections resulting from relativistic effects are considered, and some uncertainties inherent in previous work are clarified.