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

## TL;DR

This paper investigates how nuclear medium effects influence the ratio of longitudinal to transverse cross sections and the Callan-Gross relation in nuclei, using a microscopic model and comparing with experimental data.

## Contribution

It provides a detailed theoretical analysis of nuclear medium effects on $R_A$ and CGR, incorporating various nuclear phenomena and making predictions for future experiments.

## Key findings

- Nuclear medium effects significantly modify $R_A(x,Q^2)$.
- Theoretical results agree with existing experimental data.
- Predictions for $R_A$ in future experimental kinematic regions.

## Abstract

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.