Structure function of the nucleus in the perturbative QCD with $N_c\to\infty$ (BFKL pomeron fan diagrams)

. Equation for the sum of BFKL pomeron fan diagrams is rederived by direct summation and solved numerically for rapidities y ≤ 50. At high rapidities y > 20 the resulting cross-sections for the scattering of a longitudinally polarized q ¯ q pair on the nucleus cease to depend on its transverse dimension and tend to a constant limit 0.1768 R 2 A , which corresponds to scattering of a colour dipole on a black disk. Thus the unitarity is restored and the singularity in the j plane is reduced to a simple pole at j = 1. The nuclear structure function at small x behaves as Q 2 ln(1 /x ). The found gluon density has a soliton-like form in the log k space: its form is close to Gaussian, independent of rapidity, the center moving towards higher log k with a nearly constant velocity as rapidity increases.