Nuclear binding, correlations, and the $A$-dependence of the EMC effect

Abstract

The measurements of inclusive electron scattering from nuclear targets carried out at the Thomas Jefferson National Accelerator Facility in the mid 2000s have provided valuable novel information on the $A$-dependence of the modifications of nuclear structure functions known as EMC effect.We argue that these data are best described in terms of the scaling variable $\widetilde{y}$, designed to take into account dynamical effects in interacting many-particle systems, and analyse the $A$-dependence of the slope of the inclusive cross section ratios, $R_A = (σ_A/A)/(σ_2/2)$, providing a measure of the size of the EMC effect in the region where nuclear binding plays a leading role. The results of our study reveal a linear correlation between $dR_A(\widetilde{y})/d\widetilde{y}$ and the average nucleon removal energy $\langle E_A \rangle$. The role of correlation effects in the determination of $\langle E_A \rangle$ is highlighted.

Figures (4)

• Figure 1: Inclusive cross section per nucleon of [2][]H (circles) and [12][]C (triangles) at $E_e = 5.77$ GeV, $\theta_e = 40$ deg and $4 \lesssim Q^2 \lesssim 5.6 \ {\rm GeV}^2$. The JLab data, originally reported by the E03-103 and E02-019 Collaborations in Refs. Seely09 and Nadia2012, are taken from the compilation of Ref. archive:qe. Error bars are not visible on the scale of the plot; the lines connecting the data points are meant to guide the eye.
• Figure 2: Ratio of the inclusive cross section per nucleon of [2][]H and [12][]C at $E_e = 5.77$ GeV, $\theta_e = 40$ deg and $3 \lesssim Q^2 \lesssim 6 \ {\rm GeV}^2$ reported in Refs. Seely09Nadia2012 and compiled in Ref. archive:qe. The data are displayed as a function of the scaling variable $\widetilde{y}$ of Eq.\ref{['def:ytilde']}.
• Figure 3: Slopes of the EMC ratios in the ${\widetilde{y}}$ region corresponding to $0.35 \leq x \leq 0.7$, labeled according to the nuclear mass number $A$. Diamond and circles— with the latter being offset by 0.8 MeV for clarity— represent the results obtained from JLab Arrington12 and SLAC Gomez94 data, respectively. The nuclear matter result, represented by the square, has been obtained from the EMC ratio reported in Ref. NM_EMC.
• Figure 4: Slopes of the EMC ratios in the ${\widetilde{y}}$ region corresponding to $0.35 \leq x \leq 0.7$, labelled according to the nuclear mass number $A$. The average removal energies are obtained with the $\Delta$-full $\chi$EFT Hamiltonian NV2+3-Ia. Diamond and circles— with the latter being offset by 0.4 MeV for clarity— represent the results obtained from JLab Arrington21 and SLAC Gomez94 data, respectively.