Comparison of recoil polarization in the $^{12}{rm C}(vec{e},{e}vec{p})$ process for protons extracted from $s$ and $p$ shell

We present first measurements of the double ratio of the polarization transfer components $(P^{prime}_{!x} !/ P^{prime}_{!z} )_p/ (P^{prime}_{!x} !/ P^{prime}_{!z} )_s$ for knock-out protons from $s$ and $p$ shells in $^{12}{rm C}$ measured by the $^{12}{rm C}(vec{e},{e}vec{p},)$ reaction in quasi-elastic kinematics. The data are compared to theoretical predictions in relativistic distorted-wave impulse approximation. Our results show that differences between $s$- and $p$-shell protons, observed when compared at the same initial momentum (missing momentum) largely disappear when the comparison is done at the same proton virtuality. We observe no density-dependent medium modifications for protons from $s$ and $p$ shells with the same virtuality in spite of the large differences in the respective nuclear densities.