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

Abstract

We present first measurements of the double ratio of the polarization transfer components $(P_x^{\prime }/P_z^{\prime }{)}_p/(P_x^{\prime }/P_z^{\prime }{)}_s$ for knock-out protons from $s$ and $p$ shells in ${}^{12}\mathrm{C}$ measured by the ${}^{12}\mathrm{C}(\vec{e},e^{\prime }\vec{p})$ 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.