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Many Body Problem

  
Figure: Momentum distribution of protons in 208Pb. The solid curve is a mean-field prediction.
\begin{figure}\epsfig{file=hadron/fig1.eps, width=\columnwidth}\end{figure}
 

The last decade has been marked by a remarkable interplay between many-body theory and high precision electron scattering experiments. The nuclear response has been measured at high momentum and into the continuum. Fig.[*] represents the momentum distribution of protons in 208 Pb measured at NIKHEF. The data have been extended to 500 MeV/c where the effect of correlations is clearly seen at high nucleon momentum. The partial occupancy of mean-field orbits ( $\simeq70\ \%$) is one of the cleanest signatures of nucleon-nucleon correlations. The virtual collision of two nucleons to unoccupied states produces a depletion of the states below the Fermi energy and populates the states above. The central problem is now to understand the effect of correlations on nucleon distributions and other observables. High resolution experiments using the $eA\rightarrowe^{\prime }p(A-1)$ and $eA\rightarrow e^{\prime }pp(A-2)$ reactions will allow us to probe very high momentum components and separate the longitudinal and transverse components of the nuclear response. Clear evidence for the direct knock-out of a correlated proton pair in a heavy nucleus has been observed in the reaction 16O(e,e'pp) at NIKHEF. Using large solid angle detectors, the angular correlation between the two emitted protons was determined with sufficient precision to extract information on the relative wave function of a proton pair moving in the 1p shell in 16O. The measured energy spectrum up to 20 MeV and momentum distributions are clear evidence for the direct knock-out of pp pairs in the 1s and 1p relative states (Fig.[*]). Such results demonstrate that high luminosity and high resolution, continuous beam electron accelerators will be able to extract a wealth of new information on short-range nucleon-nucleon interactions in nuclei.

  
Figure: Excitation spectrum measured in the 16O(e,e'pp) reaction. The solid curve is a fit to the data containing the following contributions: 1S (dashed), 1P (dotted) and continuum (dot-dashed).
\begin{figure}\epsfig{file=hadron/fig2.eps, width=\columnwidth}\end{figure}
 

For few-nucleon systems, calculations that take into account realistic nucleon-nucleon interactions and mesonic degrees of freedom have made impressive progress, particularly for continuum states. Future experiments involving polarised electrons and polarised nuclei, will allow experiments to unravel the spin structure of light nuclei. Elucidating the short-distance structure of nuclei will be a topic of special interest. One will study in particular how nucleon properties are affected by the nuclear medium. The study of the Coulomb sum-rule in quasi-free inclusive electron scattering shows that down to distances of 0.5 fm, nucleons in their ground state are little affected by the nuclear medium. At shorter distances, nucleons can no longer be considered as rigid objects, and one would like to understand the effect of the nuclear medium on their quark structure. 


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