The effects of the final state interaction (FSI) in semi inclusive deep inelastic electron scattering processes $A(e,ep)X$ off nuclei are investigated in details. Proton production is described within the spectator and the target fragmentation mechanisms whose relevance to the experimental study of the deep inelastic structure functions of bound nucleons and the non perturbative hadronization process is analyzed. Particular attention is paid to the deuteron target within kinematical conditions corresponding to the available and forthcoming experimental data at Jlab. We argue that there are kinematical regions where FSI effects are minimized, allowing for a reliable investigation of the DIS structure functions, and regions where the interaction of the quark-gluon debris with nucleons is maximized, which makes it possible to study hadronization mechanisms. Nuclear structure has been described by means of realistic wave functions and spectral functions and the final state interaction has been treated within an eikonal approximation approach which takes into account the rescattering of the quark-gluon debris with the residual nucleus and, in the case of complex nuclei, within an optical potential approach to account for the FSI of the struck proton.
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