Direct Observation of Proton-Neutron Short-Range Correlation Dominance in Heavy Nuclei

We measured the triple coincidence $A(e,e^{\prime }np)$ and $A(e,e^{\prime }pp)$ reactions on carbon, aluminum, iron, and lead targets at $Q^2>1.5(\mathrm{GeV}/c{)}^2$, $x_B>1.1$ and missing momentum $>400\mathrm{MeV}/c$. This was the first direct measurement of both proton-proton ($pp$) and neutron-proton ($np$) short-range correlated (SRC) pair knockout from heavy asymmetric nuclei. For all measured nuclei, the average proton-proton ($pp$) to neutron-proton ($np$) reduced cross-section ratio is about 6%, in agreement with previous indirect measurements. Correcting for single-charge exchange effects decreased the SRC pairs ratio to $\sim 3\%$, which is lower than previous results. Comparisons to theoretical generalized contact formalism (GCF) cross-section calculations show good agreement using both phenomenological and chiral nucleon-nucleon potentials, favoring a lower $pp$ to $np$ pair ratio. The ability of the GCF calculation to describe the experimental data using either phenomenological or chiral potentials suggests possible reduction of scale and scheme dependence in cross-section ratios. Our results also support the high-resolution description of high-momentum states being predominantly due to nucleons in SRC pairs.

Figure 1

Diagrammatic representation and kinematics of the triple-coincidence $A(e,e^{\prime }Np)$ reaction within the SRC breakup model. Dashed red lines represent off-shell particles. Open ovals represent undetected systems. Solid black lines represent detected particles. The momentum and energy of the particles is also indicated. See text for details.

Figure 2

Extracted reduced cross-section ratios $R$ for $pp$ to $np$ SRC pair knockout as a function of recoil proton momenta. Different filled symbols mark different nuclei. The black dashed lines show the average cross-section ratio for all four nuclei and their horizontal extents show the width of each recoil proton momenta bin. The open symbols show the results of GCF calculations for ${}^{12}\mathrm{C}$ using three different NN interactions. The inner (green) and outer (yellow) bands represent the 68% and 95% confidence ranges of the calculation. The points with dashed error bars correspond to GCF calculations using the old $pp$ to $np$ contact ratios of Ref. [28] and the points with the solid error bars use new contact ratios fit to this data set. See text for details.

Figure 3

Extracted ratios of $pp$- to $np\text{−}\mathrm{SRC}$ pairs plotted versus atomic weight $A$. The filled green circles show the ratios of $pp$- to $np\text{−}\mathrm{SRC}$ pairs extracted from $(e,e^{\prime }pp)/(e,e^{\prime }pn)$ cross-section ratios corrected for SCX using Eq. (2). The shaded regions mark the 68% and 95% confidence limits on the extraction due to uncertainties in the measured cross-section ratios and SCX correction factors (see Supplemental Material [48] for details). The magenta triangle shows the carbon data of Ref. [20], which were also corrected for SCX. The open black squares show the indirect extraction of Ref. [3]. The uncertainties on both previous extractions mark the 68% (i.e., $1\sigma$) confidence limits. The horizontal dashed lines show the ${}^{12}\mathrm{C}$ GCF-calculated contact ratios for different NN potentials using contact values fitted directly to the measured cross-section ratios. See text for details.