Extracting the mass dependence and quantum numbers of short-range correlated pairs from $A(e,e^{\prime }p)$ and $A(e,e^{\prime }pp)$ scattering

The nuclear mass dependence of the number of short-range correlated (SRC) proton-proton $\left(pp\right)$ and proton-neutron $\left(pn\right)$ pairs in nuclei is a sensitive probe of the dynamics of short-range pairs in the ground state of atomic nuclei. This work presents an analysis of electroinduced single-proton and two-proton knockout measurements off ${}^{12}\mathrm{C}$, ${}^{27}\mathrm{Al}$, ${}^{56}\mathrm{Fe}$, and ${}^{208}\mathrm{Pb}$ in kinematics dominated by scattering off SRC pairs. The nuclear mass dependence of the observed $A(e,e^{\prime }pp)/{}^{12}\mathrm{C}(e,e^{\prime }pp)$ cross-section ratios and the extracted number of $\mathit{pp}$- and $\mathit{pn}$-SRC pairs are much softer than the mass dependence of the total number of possible pairs. This is in agreement with a physical picture of SRC affecting predominantly nucleon-nucleon pairs in a nodeless relative-$S$ state of the mean-field basis.

Figure 1

Distribution (in arbitrary units) of the cosine of the angle $\gamma$ between the missing momentum of the leading proton and the recoil proton for ${}^{12}\mathrm{C}$ (dark blue long-dashed line), ${}^{27}\mathrm{Al}$ (red dotted line), ${}^{56}\mathrm{Fe}$ (purple solid line), and ${}^{208}\mathrm{Pb}$ (blue dashed line). The black dashed line shows the distribution of the random phase-space extracted from mixed events.

Figure 2

The mass dependence of the $A(e,e^{\prime }pp){/}^{12}\mathrm{C}(e,e^{\prime }pp)$ cross-section ratios. The points show the measured, FSI-uncorrected, cross-section ratios. The lower orange band and upper grey line denote ZRA reaction-model calculations for ${}^{12}\mathrm{C}$, ${}^{27}\mathrm{Al}$, ${}^{56}\mathrm{Fe}$, and ${}^{208}\mathrm{Pb}$ based on Eq. (3) with and without FSI corrections respectively. The width of the ZRA-RMSGA band reflects the maximum possible effect of SCX.

Figure 3

Mass dependence of the number of $\mathit{pp}$ (top panel) and $pn$ (bottom panel) SRC pairs of nucleus $A$ relative to ${}^{12}\mathrm{C}$. Data (small black circles with error bars) are extracted from the measured CLAS $A(e,e^{\prime }p)$ and $A(e,e^{\prime }pp)$ cross-section ratios [8, 21] after correcting for FSI. Error bars include the estimated uncertainty on the cross-section ratios and the FSI corrections. The green squares correspond with unconditional counting of the $pp$ pairs, i.e., $\left[Z\right(Z-1)/30$ in the upper panel] and $pn$ pairs ($ZN/36$ in the bottom panel) for the nuclei ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, ${}^{27}\mathrm{Al}$, ${}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}$, ${}^{56}\mathrm{Fe}$, ${}^{63}\mathrm{Cu}$, ${}^{108}\mathrm{Ag},$ and ${}^{208}\mathrm{Pb}$. The yellow diamonds are the ratios obtained by counting IPM pairs in a relative $S$ and $P$ state. The blue triangles count IPM $S_{n=0}$ pairs. The solid line denotes the result of a reaction-model calculation for scattering from close-proximity pairs [Eq. (3)] which takes full account of the experimental phase space. This calculation does not include FSI corrections because these are applied to the data, see text for details.