QCD evolution of the gluon density in a nucleus

The Glauber approach to the gluon density in a nucleus, suggested by A. Mueller, is developed and studied in detail. Using the GRV parameterization for the gluon density in a nucleon, the value as well as energy and $Q^2$ dependence of the gluon density in a nucleus is calculated. It is shown that the shadowing corrections are under theoretical control and are essential in the region of small $x$. They change crucially the value of the gluon density as well as the value of the anomalous dimension of the nuclear structure function, unlike of the nucleon one. The systematic theoretical way to treat the correction to the Glauber approach is developed and a new evolution equation is derived and solved. It is shown that the solution of the new evolution equation can provide a selfconsistent matching of ``soft" high energy phenomenology with ``hard" QCD physics.