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

Abstract

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 2 H( 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) 1 H is largely canceled out, as shown for both 2 H and 12 C data. This implies that the difference between the restingand the moving-proton kinematics is not the primary cause for the deviations between quasi-elastic and elastic scattering reported previously.

Quasi-elastic polarization-transfer measurements on the deuteron in anti-parallel kinematics

“…The dependence of the polarization transfer components and their ratios on Q 2 (due to the form factors) and other kinematic effects are reduced by dividing the measured values by the expected ones for elastic ep scattering with similar kinematics [13][14][15]27]. We use the "moving-proton" prescription [27,28], rather than the expressions for elastic scattering off a resting proton [10]. In this prescription, each measured quasi-elastic event is compared to an elastic event that has the same incident electron energy (k 0 ), the same magnitude of the four-momentum transfer (Q 2 ), and the same initial proton momentum (− p miss ) as the measured quasi-elastic event.…”

“…In this prescription, each measured quasi-elastic event is compared to an elastic event that has the same incident electron energy (k 0 ), the same magnitude of the four-momentum transfer (Q 2 ), and the same initial proton momentum (− p miss ) as the measured quasi-elastic event. Full details on the expressions for the polarization transfer observables are given in [27,28]. In Fig.…”

“…More details are found in the supplementary. [27,28] to those for free resting protons [10], using the kinematics derived from measured events in 2 H( e, e p)n reactions reported in this work (closed symbols) and in [13,14] (open symbols).…”

“…Following the convention used in [13][14][15]27] we use the struck-proton virtuality ("off-shellness"), ν, as our parameter of choice. The virtuality is defined as [13]:…”

“…We extracted the ratios of the polarization-transfer components for the deuteron to those of a free proton, (Px) (Px/Pz) 1 H , where the denominator expressions are calculated event-by-event using free moving-proton kinematics [27,28]. These ratios are shown as functions of ν in Fig.…”