$\pi^+\pi^-$ Emission from Coherent $\rho^0$ Propagation in Nuclei

Cross sections for the $\pi^+\pi^-$ events arising due to the decay of $\rho^0$ meson have been calculated. This rho meson is considered to produce coherently in the $(p,p^\prime)$ reaction on a nucleus. The distorted wave functions for the continuum particles and the rho meson propagator are described by the eikonal form. The sensitivity of the cross section on the pion emission angle as well as on the beam energy has been investigated. The cross sections for the $\rho^0$ decaying inside and outside the nucleus are compared. In addition, the coherent and incoherent contributions to the cross section due to $\rho^0$ inside and outside decay amplitudes are presented. The initial and final state interactions for this reaction have been studied. The nuclear medium effect on the $\rho^0$ propagation through the nucleus is also explored.