Nuclear transparencies with a two step process of the $A(e,e'π^+)$ reactions

Nuclear transparency in pion-induced nuclear reactions has been investigated on the basis of Glauber multiple scattering theory considering a two-step process within the framework of vector meson dominance (VMD). In the present context, the application of the quantum diffusion model (QDM) to the Glauber theory plays a role in explaining the dependence of the transparency on the four momentum transfer squared $Q^2$. % as shown in the experimental data. The short-range correlation (SRC) considered further gives the contribution to the magnitude of the transparency by a constant amount independent of the $Q^2$ variation, and the results from the QDM and SRC overestimate the experimental data. The inclusion of the two-step process with the $\rho N$ scattering cross section, $\sigma_{\rho N}=3 $ mb has the effect of reducing the transparency and thus leads to a good agreement with the experimental data on the reaction $A(e,e'\pi^+)$ for $^{12}$C, $^{27}$Al, $^{63}$Cu and $^{197}$Au nuclei.