Large $Q^2$ electrodisintegration of the deuteron in the virtual nucleon approximation

The two-body breakup of the deuteron is studied at high-$Q^2$ kinematics, with the main motivation to probe the deuteron at small internucleon distances. Such studies are associated with the probing of the high-momentum component of the deuteron wave function. For this, two main theoretical issues have been addressed: electromagnetic interaction of the virtual photon with the bound nucleon and the strong interaction of produced baryons in the final state of the breakup reaction. Within virtual nucleon approximation we developed a new prescription to account for the bound nucleon effects in electromagnetic interaction. The final-state interaction at high-$Q^2$ kinematics is calculated within the generalized eikonal approximation (GEA). We studied the uncertainties involved in the calculation and performed comparisons with the first experimental data on deuteron electrodisintegration at large $Q^2$. We demonstrate that the experimental data confirm the GEA’s early prediction that the rescattering is maximal at $~$${70}^{°}$ of recoil nucleon production relative to the momentum of the virtual photon. Comparisons also show that the forward recoil nucleon angles are best suited for studies of the electromagnetic interaction of bound nucleons and the high-momentum structure of the deuteron. Backward recoil angle kinematics show sizable effects owing to the $\Delta$-isobar contribution. The latter indicates the importance of further development of the GEA to account for the inelastic transitions in the intermediate state of the electrodisintegration reactions.

Figure 1

GEA diagrams.

Figure 2

Elastic ${\gamma }^{*}d\to d^{\prime }$ diagram.

Figure 3

Dependence of ratio $R$ on the recoil angle of the neutron for different values of $p_r=100$, 200, 300, 400, 500 MeV/$c$ and $Q^2=2$, 6 GeV${}^2$. Solid line, unfactorized approximations; dashed line, factorized approximations.

Figure 4

Dependence of ratio $R$ on the recoil angle of the neutron for different values of $p_r$ and $Q^2=2$, 6 GeV${}^2$. The recoil neutron momenta are the same as in Fig. 3. Solid line, unfactorized calculation with the pole term only in the FSI amplitude; dashed line, unfactorized approximations with both pole and principal value terms in the FSI amplitude.

Figure 5

Dependence of ratio $R$ on the recoil angle of the neutron for different values of $p_r$ and $Q^2=2$, 6 GeV${}^2$. The recoil neutron momenta are the same as in Fig. 3. Solid line, unfactorized approximation with the pole term only forward $\mathit{pn}\to \mathit{pn}$ rescattering; dashed line, unfactorized approximation including the pole terms for both forward $\mathit{pn}\to \mathit{pn}$ and charge-exchange $\mathit{pn}\to \mathit{np}$ rescattering amplitudes.

Figure 6

Ratio of PWIA cross sections calculated using on-shell and off-shell approximations for the electromagnetic current of the proton. The curves, from top to bottom, correspond to recoil neutron momenta of 100, 200, 300, 400, 500, 600, and 700 MeV/$c$, respectively.

Figure 7

Missing momentum dependence of the reduced cross section. The data are from Ref. [25]. Dashed line, PWIA calculation; dotted line, PWIA$+$only pole term of forward FSI; dash-dotted line, PWIA$+$forward FSI; solid line, PWIA$+$forward and charge-exchange FSI; and solid line with squares, same as the previous solid line, plus the contribution from the mechanism in which the proton is a spectator and the neutron was struck by the virtual photon.

Figure 8

Dependence of the differential cross section on the direction of the recoil neutron momentum. The data are from Ref. [26]. Dashed line, PWIA calculation; dotted line, PWIA$+$pole term of forward FSI; dash-dotted line, PWIA$+$forward FSI; solid line, PWIA$+$forward and charge-exchange FSI. The momentum of the recoil neutron is restricted to $200<p_r<300$ MeV/$c$. The labels 2, 3, 4, and 5 correspond to the values of $Q^2=2\pm 0.25$, $3\pm 0.5$, $4\pm 0.5$, and $5\pm 0.5$ GeV${}^2$.

Figure 9

Dependence of the differential cross section on the direction of the recoil neutron momentum. The data are from Ref. [26]. Dashed line, PWIA calculation; dotted line, PWIA$+$pole term of forward FSI; dash-dotted line, PWIA$+$forward FSI; solid line, PWIA$+$forward and charge-exchange FSI. The momentum of the recoil neutron is restricted to $400<p_r<600$ MeV/$c$. The labels 2, 3, 4, and 5 correspond to the values of $Q^2=2\pm 0.25$, $3\pm 0.5$, $4\pm 0.5$, and $5\pm 0.5$ GeV${}^2$, respectively. The data sets and calculations for 4 and 5 are multiplied by 0.5 and 0.25, respectively.