Investigation of Proton-Proton Short-Range Correlations via the ${}^{12}\mathrm{C}(e,e^{\prime }pp)$ Reaction

We investigated simultaneously the ${}^{12}\mathrm{C}(e,e^{\prime }p)$ and ${}^{12}\mathrm{C}(e,e^{\prime }pp)$ reactions at $Q^2=2(\mathrm{GeV}/c{)}^2$, $x_B=1.2$, and in an ($e$, $e^{\prime }p$) missing-momentum range from 300 to $600\mathrm{MeV}/c$. At these kinematics, with a missing momentum greater than the Fermi momentum of nucleons in a nucleus and far from the delta excitation, short-range nucleon-nucleon correlations are predicted to dominate the reaction. For $(9.5\pm 2)\%$ of the ${}^{12}\mathrm{C}(e,e^{\prime }p)$ events, a recoiling partner proton was observed back-to-back to the ${}^{12}\mathrm{C}(e,e^{\prime }p)$ missing-momentum vector, an experimental signature of correlations.

Figure 1

A vector diagram of the layout of the ${}^{12}\mathrm{C}(e,e^{\prime }pp)$ experiment shown for the largest $p_{\mathrm{miss}}$ kinematics of $0.55\mathrm{GeV}/c$.

Figure 2

The measured ${}^{12}\mathrm{C}(e,e^{\prime }p)$ missing-energy spectrum for $p_{\mathrm{miss}}\sim 0.31\mathrm{GeV}/c$. The peak at 16 MeV is due to removal of $p$-shell protons leaving the ${}^{11}\mathrm{B}$ in its ground state. The shaded region contains events with residual excited bound or continuum states. The dashed line contains events in which the $\Delta$ was excited. Inserted is the TOF spectrum for protons detected in BigBite in coincidence with the ${}^{12}\mathrm{C}(e,e^{\prime }p)$ reaction. The random background is shown as a dashed line.

Figure 3

The distribution of the cosine of the opening angle between the ${\overrightarrow{p}}_{\mathrm{miss}}$ and ${\overrightarrow{p}}_{\mathrm{rec}}$ for the $p_{\mathrm{miss}}=0.55\mathrm{GeV}/c$ kinematics. The histogram shows the distribution of random events. The curve is a simulation of the scattering off a moving pair with a width of $0.136\mathrm{GeV}/c$ for the pair c.m. momentum.

Figure 4

The measured and extrapolated ratios of yields for the ${}^{12}\mathrm{C}(e,e^{\prime }pp)$ and the ${}^{12}\mathrm{C}(e,e^{\prime }p)$ reactions. The full squares are the yield ratios and the open squares are the corresponding ratios of the differential cross section for the ${}^{12}\mathrm{C}(e,e^{\prime }pp)$ reaction to that of the ${}^{12}\mathrm{C}(e,e^{\prime }p)$ reaction. A simulation was used to account for the finite acceptance of BigBite and make the extrapolation to the total number of recoiling proton pairs shown in lower figure. The gray area represents a band of $\pm 2\sigma$ uncertainty in the width of the c.m. momentum of the pair.