Nuclear dependence of $R=\frac{\sigma_L}{\sigma_T}$ and Callan-Gross relation in nuclei

The electromagnetic nuclear structure functions $F_{1A} (x,Q^2)$, $F_{2A} (x,Q^2)$ and $F_{LA} (x,Q^2)$ have been calculated using a microscopic model of nucleus to study the nuclear medium effects on the ratio $R_A(x,Q^2)=\frac{\sigma_{LA} (x,Q^2)}{\sigma_{TA} (x,Q^2)} = \frac{F_{LA} (x,Q^2)}{2xF_{1A} (x,Q^2)}$ and the Callan-Gross relation(CGR) in nuclei. The nuclear medium effects due to the Fermi motion, binding energy, nucleon correlations, mesonic contribution and shadowing have been taken into account. The theoretical results for the nuclear dependence of $R_{A} (x,Q^2)$ and its impact on CGR have been presented and compared with the available experimental data on the various nuclear targets. The predictions have been made for $R_{A} (x,Q^2)$ in the kinematic region of $x$ and $Q^2$ for some nuclei relevant for the future experiments to be performed at the JLab.