Induced Polarization in $^4$He$(e,e' \vec p)^3$H*

Polarization transfer in the $^4$He($\vec e,e^\prime \vec p\,$)$^3$H reaction up to $Q^2 = 2.6$ (GeV/c)$^2$ has been measured in an attempt to study possible medium modifications of the proton form factors. Indeed, the measured ratio of polarization-transfer coefficients are described by the inclusion of a medium modification of the proton form factors. This interpretation is challenged by a recent calculation including, particularly, a spin-dependent charge exchange in the final-state interaction. The induced polarization in this reaction is a measure of final-state interactions. Precise data on these are key to shed more light on this controversy. In our recent follow-up experiment E03-104 at Jefferson Lab data were taken at a $Q^2$ of 0.8 (GeV/c)$^2$ and 1.3 (GeV/c)$^2$ on $^1$H and $^4$He targets. The extraction of the small induced polarization of the recoiling proton for the $^4$He$(e,e'\vec p)$ reaction is complicated by the possible presence of instrumental asymmetries in the focal-plane polarimeter. The induced polarization in the elastic $^1$H$(e,e'\vec p)$ reaction is (in one-photon approximation) zero and provides crucial information about these false asymmetries. Our extraction procedure and preliminary results will be presented.