Skewed recoil polarization in (e,e'p) reactions from polarized nuclei

The general formalism describing $\vec{A}(\vec{e},e'\vec{p})B$ reactions, involving polarization of the electron beam, target and ejected proton, is presented within the framework of the relativistic plane wave impulse approximation for medium and heavy nuclei. It is shown that the simultaneous measurement of the target and ejected proton polarization can provide new information which is not contained in the separate analysis of the $\vec{A}(\vec{e},e'p)B$ and $A(\vec{e},e'\vec{p})B$ reactions. The polarization transfer mechanism in which the electron interacts with the initial nucleon carrying the target polarization, making the proton exit with a fractional polarization in a different direction, is referred to here as ``skewed polarization''. The new observables characterizing the process are identified, and written in terms of polarized response functions and asymmetries which are of tensor nature. The corresponding half-off-shell single-nucleon responses are analyzed using different prescriptions for the electromagnetic vertex and for different kinematics. Numerical predictions are presented for selected perpendicular and parallel kinematics in the case of $^{39}$K as polarized target.