On the gluon shadowing effect in light and heavy nuclei at small $x$

We propose new Transverse Momentum Dependent (TMD) gluon densities in nuclei. Our method is based on a combination of the color dipole scattering formalism, within which we interpret the nuclear deep inelastic structure functions $F_2^{A}(x, Q^2)$ and well established property of geometrical scaling from nucleons to nuclei. As an input, we employ the TMD gluon density in a proton which provides a self-consistent simultaneous description of the numerous HERA and LHC data on $pp$, $ep$ and $\gamma p$ processes. After fitting the relevant phenomenological parameters to the experimental data on the ratios $F_2^{A}(x, Q^2)/F_2^{A^\prime}(x, Q^2)$ for several nuclear targets $A$ and $A^\prime$, we derive the corresponding nuclear gluon distributions. Then, we make predictions for gluon shadowing effects at small Bjorken $x$ in their dependence of the mass number $A$. A comparison with other approaches is given.