Comparison of forward and backward $pp$ pair knockout in ${}^3$He$(e,e^{\prime }pp)n$

Measuring nucleon-nucleon short range correlations (SRCs) has been a goal of the nuclear physics community for many years. They are an important part of the nuclear wave function, accounting for almost all of the high-momentum strength. They are closely related to the EMC effect. While their overall probability has been measured, measuring their momentum distributions is more difficult. In order to determine the best configuration for studying SRC momentum distributions, we measured the ${}^3$He$(e,e^{\prime }pp)n$ reaction, looking at events with high-momentum protons ($p_p>0.35$ GeV/c) and a low-momentum neutron ($p_n<0.2$ GeV/c). We examined two angular configurations: either both protons emitted forward or one proton emitted forward and one backward (with respect to the momentum transfer, $\vec{q}$). The measured relative momentum distribution of the events with one forward and one backward proton was much closer to the calculated initial-state $pp$ relative momentum distribution, indicating that this is the preferred configuration for measuring SRC.

Figure 1

Missing mass for ${}^3$He$(e,e^{\prime }pp)$$X$ for missing momentum $p_X<0.2$ GeV/c. The dashed vertical line indicates the neutron missing mass cut of $M_X<1.05$ GeV/c${}^2$.

Figure 2

The square of the four-momentum transfer, $Q^2$, versus the energy transfer $\nu$ for ${}^3$He$(e,e^{\prime }pp)n$ events with $p_n⩽0.2$ GeV/c. The points show the data, the straight line shows quasielastic kinematics where $x=Q^2/2m\nu =1$. The lower limit at $Q^2\approx 1$ GeV${}^2$ is due to the CLAS acceptance.

Figure 3

(a) The number of counts as a function of opening angle between the two protons in the laboratory frame for ${}^3$He$(e,e^{\prime }pp)n$ events for $p_n<0.2$ GeV/c for data (solid histogram) and the one-body calculation of Laget integrated over the experimental acceptance with arbitrary normalization (dashed histogram). (b) The number of counts as a function of the two proton-momentum transfer angles, ${\theta }_{p_{1}q}$ and ${\theta }_{p_{2}q}$.

Figure 4

The relevant graphs in the diagrammatic calculation of the ${}^3$He$(e,e^{\prime }pp)n$ reaction [21, 22, 23, 24] including one-body, two-body, and three-body mechanisms. The graph corresponding to final-state interactions (as the term is used in this paper) is the middle graph on the left side.

Figure 5

${}^3$He$(e,e^{\prime }pp)n$ events with $p_n<0.2$ GeV/c and $0.4⩽p_p^{\mathrm{slow}}⩽0.6$ GeV/c (where $p_p^{\mathrm{slow}}$ is the smaller of the two proton momenta): (a) The number of counts plotted versus $\cos {\theta }_{nq}$, the angle between the neutron momentum and $\vec{q}$. The points show the data, the dotted curve shows Laget's one-body calculation, the dashed curve includes final-state interactions, and the solid curve shows the full calculation including FSI and meson exchange currents [21, 22, 23, 24]. For ease of comparison of the angular distributions, the theoretical calculations are all multiplied by the same arbitrary factor to approximately scale the full calculation to the data. The data and the calculations are all approximately isotropic. (b) The number of counts plotted as a function of the four-momentum transfer squared and the energy transfer ($Q^2$ and $\nu$). The points show the data, the straight line shows quasielastic kinematics where $x=Q^2/2m\nu =1$.

Figure 6

The laboratory-frame cross section for ${}^3$He$(e,e^{\prime }pp)n$ events with $p_n<0.2$ GeV/c and $0.4⩽p_p^{\mathrm{slow}}⩽0.6$ plotted versus ${\theta }_{pq}$, the opening angle between the proton momentum, ${\vec{p}}_p^{\mathrm{slow}}$, and the momentum transfer $\vec{q}$. The points show the data, the dotted curve shows Laget's one-body calculation, the dashed curve includes final-state interactions, and the solid curve shows the full calculation including FSI and meson exchange currents [21, 22, 23, 24]. No scale factors have been applied to the calculations. Systematic uncertainties of 15$\%$ are not shown.

Figure 7

The square of the four-momentum transfer, $Q^2$, versus the energy transfer $\nu$ for ${}^3$He$(e,e^{\prime }pp)n$ events with $p_n⩽0.2$ GeV/c; (a) with two forward protons. Both protons are within 35${}^{\circ }$ of the momentum transfer, ${\theta }_{p_{1}q}$ and ${\theta }_{p_{2}q}⩽{35}^{\circ }$; and (b) with one forward and one backward proton such that ${\theta }_{pq}⩾{100}^{\circ }$. The points show the data, the straight line shows quasielastic kinematics where $x=Q^2/2m\nu =1$.

Figure 8

The angular distribution of $p_n⩽0.2$ GeV/c neutrons with respect to the momentum transfer $\vec{q}$, for ${}^3$He$(e,e^{\prime }pp)n$ events (a) with two forward protons, ${\theta }_{p_{1}q},{\theta }_{p_{2}q}⩽{35}^{\circ }$, and (b) with one backward proton ${\theta }_{pq}⩾{100}^{\circ }$. The points show the data, the histograms are the same as in Fig. 6. For ease of comparison of the angular distributions, the calculations have been separately normalized for the two plots so that the full calculation (solid line) is approximately equal to the data.

Figure 9

The ${}^3$He$(e,e^{\prime }pp)n$ laboratory-frame cross section plotted versus the $q$-subtracted relative momentum, $p_{\mathrm{rel}}=|{\vec{p}}_1-\vec{q}-{\vec{p}}_2|/2$, for events with a) both protons forward, ${\theta }_{p_{1}q},{\theta }_{p_{2}q}⩽{35}^{\circ }$ and b) one proton backward, ${\theta }_{p_{2}q}⩾{100}^{\circ }$. The points show the data, the dotted line shows the one-body calculation, the dashed line shows the one-body $+$ FSI calculation, and the solid line shows the full calculation including FSI and MEC. No scale factors have been applied to the calculations.