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 2H data measured at the Mainz Microtron (MAMI). We show the ratios of the transverse (Px) and longitudinal (Pz) components of the polarization transfer in 2H(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 (Px/Pz)A(Px/Pz)1His largely canceled out, as shown for both 2H and 12C 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