The ${}^3$${\text{He}(e,e{}^{\prime }p)}^2\text{H}$ and ${}^4$${\text{He}(e,e{}^{\prime }p)}^3\text{H}$ reactions at high momentum transfer

We present updated calculations for observables in the processes ${}^3\text{He}$($e,e^{\prime }p$)${}^2\text{H}$, ${}^4\text{He}$($e,e^{\prime }p$)${}^3\text{H}$, and ${}^4\text{He}$($\vec{e},e^{\prime }\vec{p}$)${}^3\text{H}$. This update entails the implementation of improved nucleon-nucleon ($NN$) amplitudes to describe final-state interactions (FSI) within a Glauber approximation and includes full spin-isospin dependence in the profile operator. In addition, an optical potential, which has also been updated since previous work, is utilized to treat FSI for the ${}^4\text{He}$($e,e^{\prime }p$)${}^3\text{H}$ and ${}^4\text{He}$($\vec{e},e^{\prime }\vec{p}$)${}^3\text{H}$ reactions. The calculations are compared with experimental data and show good agreement between theory and experiment. Comparisons are made between the various approximations in the Glauber treatment, including model dependence owing to the $NN$ scattering amplitudes, rescattering contributions, and spin dependence. We also analyze the validity of the Glauber approximation at the kinematics the data is available by comparing to the results obtained with the optical potential.

Figure 1

Differential cross sections for the ${}^3\text{He}$($e,e^{\prime }p$)${}^2\text{H}$ reaction at $\varphi ={180}^{\circ }$. The experimental data are compared with the plane-wave impulse approximation (PWIA) and with the full single and double rescattering Glauber approximation with MEC [GLB($1+2$) With MEC] and without MEC [GLB($1+2$) No MEC]. The profile operator in the Glauber approximation is derived from $NN$ scattering amplitudes (including central, single-spin-flip, and double-spin-flip terms), boosted from the c.m. frame to the rescattering (lab) frame. Statistical Monte Carlo errors are smaller than the symbols, and lines are drawn to guide the eye.

Figure 2

Same as Fig. 1, but at $\varphi =0^{\circ }$.

Figure 3

Same as Fig. 1, but for the longitudinal-transverse asymmetry.

Figure 4

Differential cross sections for the ${}^3\text{He}$($e,e^{\prime }p$)${}^2\text{H}$ reaction at $\varphi ={180}^{\circ }$ obtained in various approximation schemes; see text for descriptions of the approximations. Lines are drawn to guide the eye.

Figure 5

Same as Fig. 4, but at $\varphi =0^{\circ }$.

Figure 6

Ratios of differential cross sections as shown in Fig. 4.

Figure 7

Ratios of differential cross sections as shown in Fig. 5.

Figure 8

Same as Fig. 4, but for the longitudinal-transverse asymmetry.

Figure 9

Reduced differential cross section of ${}^4\text{He}$($e,e^{\prime }p$)${}^3\text{H}$ for ``CQ2'' kinematics compared to experimental data and various calculation schemes. See text for descriptions of the curves. Lines are drawn to guide the eye.

Figure 10

Same as Fig. 9, except for “PY1” kinematics.

Figure 11

Same as Fig. 9, except for “PY2” kinematics.

Figure 12

Induced polarization for ${}^4\text{He}$ compared to experimental data. The optical potential is tuned to reproduce the data. See text for descriptions of the curves. Lines are drawn to guide the eye.

Figure 13

Polarization transfer for ${}^4\text{He}$ compared to experimental data. See text for descriptions of the curves. Lines are drawn to guide the eye.

Figure 14

Differential cross sections obtained from the SAID (solid line), Ciofi (dashed line), and the central contribution from SAID (short dashed line) amplitudes for (a) $pn$ scattering and (b) $pp$ scattering for $T_{\text{lab}}=0.8\mathrm{GeV}$ ($s=5.03{\mathrm{GeV}}^2$).