Constraining the nuclear gluon distribution in $eA$ processes at RHIC

A systematic determination of the gluon distribution is of fundamental interest in understanding the parton structure of nuclei and the QCD dynamics. Currently, the behavior of this distribution at small $x$ (high energy) is completely undefined. In this paper we analyze the possibility of constraining the nuclear effects present in $xg^A$ using the inclusive observables which would be measured in the future electron-nucleus collider at RHIC. We demonstrate that the study of nuclear longitudinal and charm structure functions allows to estimate the magnitude of shadowing and antishadowing effects in the nuclear gluon distribution.