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

Abstract A comparison between polarization-transfer to a bound protonin quasi-free kinematics by the A ( e → , e ′ p → ) knockout reaction and that in elastic scatteringoff a free protoncan provide information on the characteristics of the bound proton. In the past the reported measurements have been compared to those of a free protonwith zero initial momentum. We introduce, for the first time, expressions for the polarization-transfer components when the protonis 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 H 2 ( e → , e ′ p → ) n , to those of elastic scatteringoff 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 protonmotion is up to 20% at high missing momentum. However the effect on the double ratio ( P x / P z ) A ( P x / P z ) H 1 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- protonkinematics is not the primary cause for the deviations between quasi-elastic and elastic scatteringreported previously.