Relativistic calculation of deuteron threshold electrodisintegration at backward angles

The threshold electrodisintegration of the deuteron at backward angles is studied in instant form Hamiltonian dynamics, 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. In order to estimate the magnitude of the relativistic effects we perform, for comparison, the calculation with a nonrelativistic phase-equivalent Hamiltonian and consistent 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 (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 nonrelativistic 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 nonrelativistic context, of the present electromagnetic current model to reproduce accurately the experimental data at intermediate values of momentum transfers.

Figure 1

The deuteron S- and D-state radial wave functions obtained with the R and NR Hamiltonian models.

Figure 2

The $\mathit{np}$ ${}^1{S}_0$-state radial wave functions obtained with the R and NR Hamiltonian models at a center-of-mass energy of 1.5 MeV.

Figure 3

The cross sections for deuteron threshold electrodisintegration at backward angles, obtained with the relativistic and nonrelativistic Hamiltonian models and corresponding one-body currents [curves labeled IA (R) and IA (NR)] and by ignoring boost corrections in the relativistic calculation [curve labeled IA (RNB)], are compared with the experimental data from Refs. [25, 26, 27, 28]. The inset displays the ratio of the IA (R) and IA (RNB) to the NR predictions.

Figure 4

Same as in Fig. 3, but with one-body and pion-exchange two-body currents. The cross sections obtained in the IA (R) calculation are also shown.

Figure 5

The IA$+\pi$ (R) and IA$+\pi$ (NR) predictions of Fig. 4 are compared with the results corresponding to different approximations, labeled, respectively, IA$+\pi$ (RK0), IA$+\pi$ (NRW), and IA$+\pi$ (NRC). See text for discussion. The experimental data are from Refs. [25, 26, 27, 28].

Figure 6

The cross sections for deuteron threshold electrodisintegration at backward angles, obtained in the IA (R) and IA$+\pi$ (R) calculations, are compared with the results of calculations based on the NR and R Hamiltonian models and corresponding one- and two-body currents, but including only the ${}^1{S}_0$ channel in the $\mathit{np}$ final state. The experimental data are from Refs. [25, 26, 27, 28].