The semi-inclusive deep inelastic scattering of electrons off the deuteron ($^2H equiv D$) and $^3He$ with detection of slow protons and deuterons, respectively, i.e. the processes $D(e,ep)X$ and $^3He(e,eD)X$, are calculated within the spectator mechanism, taking into account the final state interaction of the hadronizing quark with the detected protons and deuterons, respectively. It is shown that by a proper choice of the kinematics the origin of the EMC effect and the details of the interaction between the hadronizing quark and the nuclear medium can be investigated at a level which cannot be reached by inclusive deep inelastic scattering. A comparison of our calculations with recently available experimental data on the process $D(e,ep)X$ shows a good agreement in the backward hemisphere of the emitted nucleons. Theoretical predictions at the energies thyat will be available at the upgraded Thomas Jefferson National Accelerator Facilty are presented, and the possibility to investigate the proposed semi-inclusive processes at electron-ion colliders is briefly discussed.
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