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

TL;DR

This study measures and compares the polarization transfer in proton knockout from different shells in carbon-12, finding that when accounting for virtuality, the polarization ratios are similar, indicating no significant medium modifications.

Contribution

First measurements of polarization transfer ratios for s- and p-shell protons in carbon-12, showing virtuality as a key factor in comparing nuclear medium effects.

Findings

Differences between s- and p-shell protons largely vanish at the same virtuality.

No evidence of density-dependent medium modifications at equal virtuality.

Results support the importance of virtuality over local density in polarization transfer studies.

Abstract

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.