Electrodisintegration of the Deuteron. I. Connection between then−p−dVertex Function and the Deuteron Wave Function

Higher-order relativistic corrections to the Durand theory for the electrodisintegration of the deuteron are considered, based on the Mandelstam representation for the transition matrix element. The analysis concentrates on the kinematical region corresponding to the broad quasi-elastic peak in the cross section $\frac{d^2\sigma }{d{\Omega }_{e}d{e_0}^{\prime }}$, where ${e_0}^{\prime }$ is the final electron energy. The presence of anomalous thresholds and the close connection between the nonrelativistic wave functions and the spectral functions in the anomalous region allow the relativistic expression to be recast in terms of ostensibly nonrelativistic wave functions. The calculation is facilitated by separating the neutron-proton-deuteron vertex function into angular momentum components corresponding to momentum-space wave functions. The result clarifies the role of certain off-mass-shell effects, particuarly those contributions which involve antiparticles in the intermediate state. The antiparticle contributions are found to be small for $q^2\lesssim 0.8 {\left(\frac{\mathrm{BeV}}{c}\right)}^2$. The cross sections $\frac{d^2\sigma }{d{\Omega }_{e}d{e_0}^{\prime }}$ and $\frac{d^3\sigma }{d{\Omega }_{e}d{e_0}^{\prime }d\left(cos\theta \right)}$ are presented in first Born approximation but the detailed inclusion of the effects of final-state interactions on the cross sections is reserved for a subsequent paper.