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We present first measurements of the double ratio of the polarizationtransfer 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 $^{12}{\rmC}(\vec{e},{e}'\vec{p}\,)$ reaction in quasi-elastic kinematics. The data arecompared to theoretical predictions in relativistic distorted-wave impulseapproximation. Our results show that differences between $s$- and $p$-shellprotons, observed when compared at the same initial momentum (missing momentum)largely disappear when the comparison is done at the same proton virtuality. Weobserve no density-dependent medium modifications for protons from $s$ and $p$shells with the same virtuality in spite of the large differences in therespective nuclear densities.

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