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

Abstract

The role of the electron-helicity-dependent cross-section term and the structure function $f^{\prime}_{01}$ in the quasi-elastic $A(\vec{e}, e^{\prime}p)$ process was studied. The $f^{\prime}_{01}$ was measured for proton knockout from the $1\mathrm{d}_{3/2}$ shell in $^{40}\mathrm{Ca}$ via the $^{40}{\rm Ca}(\vec{e},e' p)^{39}{\rm K}_{\rm g.s.}$ 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 $f^{\prime}_{01}$ 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.