Probing the Repulsive Core of the Nucleon-Nucleon Interaction via the ${}^4\mathrm{He}(e,e^{\prime }pN)$ Triple-Coincidence Reaction

We studied simultaneously the ${}^4\mathrm{He}(e,e^{\prime }p)$, ${}^4\mathrm{He}(e,e^{\prime }pp)$, and ${}^4\mathrm{He}(e,e^{\prime }pn)$ reactions at $Q^2=2(\mathrm{GeV}/c{)}^2$ and $x_B>1$, for an $(e,e^{\prime }p)$ missing-momentum range of 400 to $830\mathrm{MeV}/c$. The knocked-out proton was detected in coincidence with a proton or neutron recoiling almost back to back to the missing momentum, leaving the residual $A=2$ system at low excitation energy. These data were used to identify two-nucleon short-range correlated pairs and to deduce their isospin structure as a function of missing momentum, in a region where the nucleon-nucleon ($NN$) force is expected to change from predominantly tensor to repulsive. The abundance of neutron-proton pairs is reduced as the nucleon momentum increases beyond $\sim 500\mathrm{MeV}/c$. The extracted fraction of proton-proton pairs is small and almost independent of the missing momentum. Our data are compared with calculations of two-nucleon momentum distributions in ${}^4\mathrm{He}$ and discussed in the context of probing the elusive repulsive component of the $NN$ force.

Figure 1

The distribution of the cosine of the opening angle $\gamma$ between the ${\overrightarrow{p}}_{\text{miss}}$ and ${\overrightarrow{p}}_{\text{recoil}}$ for the ${}^4\mathrm{He}(e,e^{\prime }pn)$ reaction ($p_{\text{miss}}=625$ and $750\mathrm{MeV}/c$ kinematics combined). The solid curve is a simulation of scattering off a moving pair with a c.m. momentum having a width of $100\mathrm{MeV}/c$. The inserts show the missing-mass distributions. In both the main figure and the inserts, the data are shown with no random background subtraction. The random background is shown as dash-dotted (red online) curves.

Figure 2

Bottom panel: the measured ratios ${}^4\mathrm{He}(e,e^{\prime }pp)/{}^4\mathrm{He}(e,e^{\prime }pn)$ shown as solid symbols, as a function of the ${}^4\mathrm{He}(e,e^{\prime }p)$ missing momentum. Each point is the result of a different setting of the detectors. The bands represent the data corrected for FSI to obtain the pair ratios, see text for details. Also shown are calculations using the momentum distribution of Ref. [10] for pairs with weighted-average c.m. momentum assuming arbitrary angles between the c.m. and the relative momenta in the pair (solid black line). The middle panel shows the measured ${}^4\mathrm{He}(e,e^{\prime }pp)/{}^4\mathrm{He}(e,e^{\prime }p)$ and extracted $\#pp/\#p$ ratios. The top panel shows the measured ${}^4\mathrm{He}(e,e^{\prime }pn)/{}^4\mathrm{He}(e,e^{\prime }p)$ and extracted $\#pn/\#p$ ratios. The unphysical region above 100% obtained due to systematic uncertainties and statistical fluctuations is marked by white strips. Ratios for ${}^{12}\mathrm{C}$ are shown as empty symbols with dashed bars. The empty star in the top panel is the BNL result [4] for ${}^{12}\mathrm{C}(p,2pn)/{}^{12}\mathrm{C}(p,2p)$.