Do nuclear reaction cross sections depend on the angle between incident beam and target-crystal?

There is indeed something similar to what you describe, the so-called blocking effect (or shadow effect) - http://www.nupecc.org/iai2001/report/C3.pdf , http://encyclopedia2.thefreedictionary.com/Blocking+Effect

EDIT (08/24/2013): Let me expand on my answer. There are at least two important effects related to propagation of charged high energy particles (or, in particular, nuclei) through a crystal: blocking effect and channeling effect. I cannot describe these effects in detail here - you can google them. What's important, this propagation strongly depends on the angles between the velocity of the particles and the crystal axes. This dependence is mostly caused by the Coulomb interaction between the particles and the atoms (electrons and nuclei) of the crystal. However, due to the modified pattern of propagation, the conditions of nuclear reactions of the particles with nuclei in the crystals can also be modified - see, e.g., Nuclear Instruments and Methods in Physics Research B 99 (1995) 440-443 (http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=12&ved=0CC4QFjABOAo&url=http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F235224869_Nuclear_reaction_channeling%2Ffile%2Fd912f510926a532e2c.pdf&ei=t5QYUumYJsiJ2AXf8YCQBw&usg=AFQjCNHbzRymgZPPk_Ii-9Bz380soA9bcA&sig2=zWghWinQfys3WwYQShnKJg&bvm=bv.51156542,d.b2I

Let's say your target is a film $10^{-2}$ mm thick. Nuclei are about $10^{-14}$ m in diamater at most. This means that the alignment of the beam with the target would have to be $10^{-9}$ radians, which is not possible with realistic beam optics. Even if your beam optics were that perfect, the perfect parallelism would be destroyed by scattering once the beam entered the target.