Summary

We propose to measure inclusive scattering at $x > 1$ on several light and heavy nuclei. The experiment will measure the cross section in the $y$-scaling region ( $Q^2 \mathrel{\raise.3ex\hbox{$>$}\mkern-14mu \lower0.6ex\hbox{$\sim$}}3$ GeV$^2$) over a large $y$ range, (corresponding to values of $x$ up to $x \approx 3$). This data is sensitive to the nucleon momentum distribution, and in particular to the high momentum components of the nucleon distribution in nuclei (probing nucleons with initial momenta in excess of 1000 MeV/c). By comparison to calculations of nuclear structure, or by direct comparisons of heavy nuclei to $^2$H and $^3$He, we will study the nature of the high momentum components to determine to what extent two nucleon correlations explain the presence of very high momentum nucleons and to what extent multinucleon correlations are required.

This data will complement the many completed and upcoming coincidence $A(e,e ^\prime p)$ and $A(e,e^\prime N N)$ measurements attempting to probe the high momentum components of the spectral function and short range correlations [43]. The inclusive measurement can reach much larger values of the missing momentum, where the coincidence measurements become cross section (or background) limited. The inclusive measurements are also cleaner, being significantly less sensitive to final state interactions, meson exchange currents, and other processes which must be modeled in the analysis of the coincidence measurements. In the inclusive measurement, one does not reconstruct the excitation energy of the final system (the missing energy of the struck nucleon), and so is sensitive to the entire missing energy distribution of the spectral function. Both inclusive and coincidence experiments are important in these studies, as inclusive measurements can provide fairly clean information on the very high momentum components of the spectral function, while the coincidence experiments can provide detailed information on the missing energy distribution (and momentum distributions for the individual shells) at lower momentum values.

In addition to the main goal of studying nucleon distributions and short range correlations in nuclei, this data will also allow us to extract the nuclear structure functions at large $x$ values. This will allow us to extend measurements of duality and scaling in nuclei, especially for $\xi > 1$ where it is not clear that $\xi$-scaling is a natural consequence of local duality. In addition, measurements of the structure function in nuclei at large values of $x$ will significantly improve the extraction of nuclear moments when combined with precision data in the deep inelastic and resonance region that will be taken in future JLab experiments [10,11].