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

Polarization transfer in quasi-elastic nucleon knockout is sensitive to the properties of the nucleon in the nuclear medium, including possible modification of the nucleon form factor and/or spinor. In our recently completed experiment E03-104 at Jefferson Lab we measured the proton recoil polarization in the $^4$He($\vec e,e^\prime \vec p\,$)$^3$H reaction at a $Q^2$ of 0.8 (GeV/$c$)$^2$ and 1.3 (GeV/$c$)$^2$ with unprecedented precision. These data complement earlier data between 0.4 and 2.6 (GeV/$c$)$^2$ from both Mainz and Jefferson Lab, in which the measured ratio of polarization-transfer coefficients differs from a fully relativistic DWIA calculation. The earlier polarization-transfer data are equally well described by the inclusion of a medium modification of the proton form factors predicted by a quark-meson coupling model and by a recent calculation including, particularly, a spin-dependent charge exchange in the final-state interaction. However, the preliminary analysis of our present data possibly implies an unexpected Q$^2$ dependence of the ratio of polarization-transfer coefficients. Due to its high statistical precision the new data allow for a detailed study of the missing momentum dependence of individual polarization-transfer coefficients in the $^4$He($\vec e,e^\prime \vec p\,$)$^3$H reaction. Final results will be discussed.