  Very recently, for the first time, the two channels of nuclear deeply virtual
Compton scattering (DVCS), the coherent and incoherent ones, have been
separated by the CLAS collaboration at JLab, using a $^4$He target. The
incoherent channel, which can provide a tomographic view of the bound proton
and shed light on its elusive parton structure, is thoroughly analyzed here in
Impulse Approximation (IA). A convolution formula for the cross sections in
terms of those for the bound proton is derived. Novel scattering amplitudes for
a bound moving nucleon have been obtained and used. A state-of-the-art nuclear
spectral function, based on the AV18 potential, exact in the two-body part,
with the recoiling system in its ground state, and modelled in the remaining
contribution, with the recoiling system in an excited state, has been used.
Different parametrizations of the generalized parton distributions of the
struck proton have been tested. A good overall agreement with the data for the
beam spin asymmetry (BSA) is obtained. It is found that the predicted
conventional nuclear effects are relevant in DVCS and in the competing
Bethe-Heitler mechanism, but they cancel each other to a large extent in their
ratio, to which the measured asymmetry is proportional. Besides, the calculated
ratio of the BSA of the bound proton to that of the free one does not describe
that estimated by the experimental collaboration. This points to possible
interesting effects beyond the IA analysis presented here. It is therefore
clearly demonstrated that the comparison of the results of a conventional
realistic approach, as the one presented here, with future precise data, has
the potential to expose quark and gluon effects in nuclei. Interesting
perspectives for the next measurements at high luminosity facilities, such as
JLab at 12 GeV and the future EIC, are addressed.
