In this talk, we reviewed several coherent diffractive processes 
with nuclear targets. They included soft hadron-nucleus diffraction,
hard inclusive diffraction in Deep Inelastic Scattering (DIS) on
nuclear targets and hard diffraction in proton-nucleus scattering.

We discussed the leading twist theory of nuclear shadowing [1,2,3,4]
and presented predictions for usual and diffractive nuclear parton
distribution functions [5].

We presented a novel method for the calculation of hard coherent 
proton-nucleus diffraction [6] using the leading twist theory of 
nuclear shadowing. We discussed the novel dramatic prediction 
that soft multiple interactions lead to very large factorization 
breaking in hard coherent pA diffraction.

We compared hard and e.m. mechanisms of hard coherent diffractive
production of two jets in pA scattering. We observed that:

 - For heavy nuclei (Pb-208) at the LHC, hard diffraction is suppressed
   compared to the e.m. machanism;
 - For lighter nuclei (Ca-40), hard diffraction is compatible to
   the e.m. machanism for the production of quark and
   gluon jets; hard diffraction is suppressed compared to the 
   e.m. machanism for heavy-quark-jets.

This suggests the following experimental strategies:

 - The use of heavy nuclei would allow to cleanly study the $\gamma p$ 
   interaction;

 - The use of lighter nuclei would allow to study factorization 
   breaking in  nuclear diffractive PDFs;

 - In the same kinematics, a comparison of diffractive dijet production to 
   heavy-quark-jet production would probe nuclear diffractive gluon PDF.

References

[1] V. Guzey, M. Strikman, hep-ph/0507310
[1] L. Frankfurt, M. Strikman, Eur. Phys. J. A 5 (1999) 293
[2] L. Frankfurt, V. Guzey, M. Strikman, J. Phys. G 27 (2001) R23
[3] L. Frankfurt, V. Guzey, M. McDermott, M. Strikman, JHEP 02 (2002) 27
[4] L. Frankfurt, V. Guzey, M. Strikman, Phys. Rev. D 71 (2005) 054001
[5] L. Frankfurt, V.Guzey , M. Strikman, Phys.  Lett.  B 586 (2004) 41
[6] V. Guzey, M. Strikman, hep-ph/0507310