Broadening of $\rho (\to e^+e^-)$ meson produced coherently in the photonuclear reaction
The $e^+e^-$ invariant mass distribution spectra are calculated to estimate the hadron parameters of the $\rho$ meson produced coherently in the photonuclear reaction. The elementary reaction occurring in the nucleus is considered to proceed as $ \gamma N \to \rho^0 N ; ~ \rho^0 \to e^+e^- $. We describe the elementary $\rho$ meson photoproduction by the experimentally determined reaction amplitude $ f_{ \gamma N \to \rho^0 N } $. The $\rho$ meson propagator is presented by the eikonal form, and the $\rho$ meson nucleus optical potential $V_{O\rho}$ appearing in it is estimated using the "$t\varrho$" approximation. The $\rho$ meson nucleon scattering amplitude $ f_{ \rho N } $ extracted from the measurements is used to generate this potential. The calculated $e^+e^-$ invariant mass distribution spectra are compared with those measured at Jefferson Laboratory. The calculated results for the transparency ratio are also presented.