The influence of Fermi motion on the comparison of the polarization transfer to a proton in elastic e→p and quasi-elastic e→A scattering

A comparison between polarization-transfer to a bound proton in quasi-free kinematics by the A(e→,e ^′ p→) knockout reaction and that in elastic scattering off a free proton can provide information on the characteristics of the bound proton. In the past the reported measurements have been compared to those of a free proton with zero initial momentum. We introduce, for the first time, expressions for the polarization-transfer components when the proton is initially in motion and compare them to the ² H data measured at the Mainz Microtron (MAMI). We show the ratios of the transverse (P _x ) and longitudinal (P _z ) components of the polarization transfer in H2(e→,e ^′ p→)n, to those of elastic scattering off a “moving proton”, assuming the proton's initial (Fermi-motion) momentum equals the negative missing momentum in the measured reaction. We found that the correction due to the proton motion is up to 20% at high missing momentum. However the effect on the double ratio [Formula presented] is largely canceled out, as shown for both ² H and ¹² C data. This implies that the difference between the resting- and the moving-proton kinematics is not the primary cause for the deviations between quasi-elastic and elastic scattering reported previously.