  Representing the semi-hard partonic interactions by the exchange of Lipatov's
perturbative Pomeron, we express the semi-hard nuclear cross section as a self
shadowing cross section. With the help of a generating functional technique, we
obtain average numbers of multiple semi-hard partonic collisions without any
need of using explicit expressions for the multi-parton distributions. The
average number of semi-hard interactions of a given projectile parton against a
target nucleus is estimated quantitatively and it is shown to grow very rapidly
above one with increasing the c.m. energy. (Figures available on request)
