Measurement of the helicity-dependent response in quasi-elastic proton knockout from ${}^{40}\mathrm{Ca}$

Abstract

The role of the electron-helicity-dependent cross-section term and the structure function $f_{01}^{\prime }$ in the quasi-elastic $A(\vec{e},e^{\prime }p)$ process was studied. The $f_{01}^{\prime }$ was measured for proton knockout from the $1{\mathrm{d}}_{3/2}$ shell in ${}^{40}\mathrm{Ca}$ via the ${}^{40}\mathrm{Ca}(\vec{e},e^{\prime }p{)}^{39}{\mathrm{K}}_{g.s.}$ reaction, leaving the residual nucleus in a well-defined state. It requires a longitudinally polarized electron beam and out-of-plane proton detection. This structure function vanishes in the absence of final-state interactions (FSI) involving the ejected proton. Presented are the dependencies of $f_{01}^{\prime }$ on the missing momentum (closely related to the initial proton's Fermi momentum) and the angle between the knocked-out proton and the virtual photon momenta. The role of the spin-orbit interaction in FSI through the $\vec{L}\cdot \vec{S}$ term in a nuclear optical potential is discussed.