Charmonium production in relativistic proton-nucleus collisions: What will we learn from the negative x_F region ?

We study the nuclear medium effects on the $c\bar{c}$ time evolution and charmonium production, in a relativistic proton-nucleus collision. In particular, we focus on the fragmentation region of the nucleus where the formation length of the charmonium mesons is shorter than the size of the nucleus. Little is known on the nuclear effects in this region. We use a quantum-mechanical model which includes a realistic potential for the $c\bar{c}$ system and an imaginary potential to describe the collisions of the $c\bar{c}$ with the nucleons. The imaginary potential introduces a transition amplitude among the charmonium states and produces an interference pattern on the charmonium survival probability, which is particulartly important for $\psi'$. Our results on the suppression factors are compared with data from the NA50 and E866/NuSea Collaborations. Predictions are given for the suppression of $J/\psi,~\psi',~\chi_c$ as a function of the nuclear mass and in the negative $x_F$ region, where data will be available soon