A relativistic calculation of the deuteron threshold electrodisintegration at backward angles

Abstract

The threshold electrodisintegration of the deuteron at backward angles is studied with a relativistic Hamiltonian, including a relativistic one-pion-exchange potential (OPEP) with off-shell terms as predicted by pseudovector coupling of pions to nucleons. The bound and scattering states are obtained in the center-of-mass frame, and then boosted from it to the Breit frame, where the evaluation of the relevant matrix elements of the electromagnetic current operator is carried out. The latter includes, in addition to one-body, also two-body terms due to pion exchange, as obtained, consistently with the OPEP, in pseudovector pion-nucleon coupling theory. The full Lorentz structure of these currents is retained. In order to estimate the magnitude of the relativistic effects we perform, for comparison, the calculation with a non-relativistic phase-equivalent Hamiltonian and the standard non-relativistic expressions for the one-body and two-body pion-exchange currents. Our results for the electrodisintegration cross section show that, in the calculations using one-body currents, relativistic corrections become significant ({\it i.e.}, larger than 10%) only at high momentum transfer $Q$ ($Q^2 \simeq 40$fm$^{-2}$ and beyond). However, the inclusion of two-body currents makes the relativistic predictions considerably smaller than the corresponding non-relativistic results in the $Q^2$ region (18--40) fm$^{-2}$. The calculations based on the relativistic model also confirm the inadequacy, already established in a non-relativistic context, of the present electromagnetic current model to reproduce accurately the experimental data at intermediate values of momentum transfers.