Polarization transfer to a bound proton in polarized electron knock-out reactions, A(e→,e′p→), is a powerful tool to look for an in-medium modification of the bound proton. It requires comparison to ...calculations that consider the many-body effects accompanying the quasi-free process. We report here measured components Px′, Pz′, and their ratio Px′/Pz′, of polarization transfer to protons bound in Ca40, which is described well by the shell model and for which reliable calculations are available. While the calculations capture the essence of the data, our statistical precision allows us to observe deviations that cannot be explained by simple scaling, including by varying the proton electromagnetic form factor ratio GE/GM. We further explore the deviations of the ratio of the polarization transfer components from that of a free proton, (Px′/Pz′)A/(Px′/Pz′)H, and its dependence on the bound-proton virtuality.
We present the first measurements of the double ratio of the polarization-transfer components (Px′/Pz′)p/(Px′/Pz′)s for knock-out protons from the s and p shells in C12 measured by the C12(e→,e′p→) ...reaction in quasi-elastic kinematics. The data are compared to theoretical predictions in the relativistic distorted-wave impulse approximation. Our results show that the differences between s- and p-shell protons, observed when compared at the same initial momentum (missing momentum), largely disappear when the comparison is done at the same proton virtuality. We observe no difference in medium modifications between protons from the s and p shells with the same virtuality in spite of the large differences in the respective nuclear densities.
We present measurements of the electron helicity asymmetry in quasi-elastic proton knockout from 2H and 12C nuclei by polarized electrons. This asymmetry depends on the fifth structure function, is ...antisymmetric with respect to the scattering plane, and vanishes in the absence of final-state interactions, and thus it provides a sensitive tool for their study. Our kinematics cover the full range in off-coplanarity angle ϕpq, with a polar angle θpq coverage up to about 8°. The missing energy resolution enabled us to determine the asymmetries for knock-out resulting in different states of the residual 11B system. We find that the helicity asymmetry for p-shell knockout from 12C depends on the final state of the residual system and is relatively large (up to ≈0.16), especially at low missing momentum. It is considerably smaller (up to ≈0.01) for s-shell knockout from both 12C and 2H. The data for 2H are in very good agreement with theoretical calculations, while the predictions for 12C exhibit differences with respect to the data.
We report the measurement of the ratio of polarization-transfer components, Px/Pz, in the H2(e→,e′p→)n reaction at low and high missing momenta, in search of differences between free and bound ...protons. The observed deviation of Px/Pz from that of a free proton, which is similar to that observed in 4He, indicates that the effect in nuclei is a function of the virtuality of the knock-out proton and the missing momentum direction, but not
the average nuclear density. There is a general agreement between the data and calculations, which assume free proton form factors, however, the measurements are consistently about 10% higher.
We measured the ratio Px/Pz of the transverse to longitudinal components of polarization transferred from electrons to bound protons in C12 by the C12(e→,e′p→) process at the Mainz Microtron (MAMI). ...We observed consistent deviations from unity of this ratio normalized to the free-proton ratio, (Px/Pz)C12/(Px/Pz)H1, for both s- and p-shell knocked out protons, even though they are embedded in averaged local densities that differ by about a factor of two. The dependence of the double ratio on proton virtuality is similar to the one for knocked out protons from H2 and He4, suggesting a universal behavior. It further implies no dependence on average local nuclear density.
We report the first measurements of the transverse (Px and Py) and longitudinal (Pz) components of the polarization transfer to a bound proton in the deuteron via the H2(e→,e′p→) reaction, over a ...wide range of missing momentum. A precise determination of the electron beam polarization reduces the systematic uncertainties on the individual components to a level that enables a detailed comparison to a state-of-the-art calculation of the deuteron using free-proton electromagnetic form factors. We observe very good agreement between the measured and the calculated Px/Pz ratios, but deviations of the individual components. Our results cannot be explained by medium modified electromagnetic form factors. They point to an incomplete description of the nuclear reaction mechanism in the calculation.
We report measurements of the induced polarization P→ of protons knocked out from 2H and 12C via the A(e,e′p→) reaction. We have studied the dependence of P→ on two kinematic variables: the missing ...momentum pmiss and the “off-coplanarity” angle ϕpq between the scattering and reaction planes. For the full 360° range in ϕpq, both the normal (Py) and, for the first time, the transverse (Px) components of the induced polarization were measured with respect to the coordinate system associated with the scattering plane. Px vanishes in coplanar kinematics, however in non-coplanar kinematics, it is on the same scale as Py.
We find that the dependence on ϕpq is sine-like for Px and cosine-like for Py. For carbon, the magnitude of the induced polarization is especially large when protons are knocked out from the p3/2 shell at very small pmiss. For the deuteron, the induced polarization is near zero at small |pmiss|, and its magnitude increases with |pmiss|. For both nuclei such behavior is reproduced qualitatively by theoretical results, driven largely by the spin-orbit part of the final-state interactions. However, for both nuclei, sizeable discrepancies exist between experiment and theory.
We present measurements of the polarization-transfer components in the H2(e→,e′p→) reaction, covering a previously unexplored kinematic region with large positive (anti-parallel) missing momentum, ...pmiss, up to 220MeV/c, and Q2=0.65(GeV/c)2. These measurements, performed at the Mainz Microtron (MAMI), were motivated by theoretical calculations which predict small final-state interaction (FSI) effects in these kinematics, making them favorable for searching for medium modifications of bound nucleons in nuclei. We find in this kinematic region that the measured polarization-transfer components Px and Pz and their ratio agree with the theoretical calculations, which use free-proton form factors. Using this, we establish upper limits on possible medium effects that modify the bound proton's form factor ratio GE/GM at the level of a few percent. We also compare the measured polarization-transfer components and their ratio for 2H to those of a free (moving) proton. We find that the universal behavior of 2H, 4He and 12C in the double ratio (Px/Pz)A(Px/Pz)H1 is maintained in the positive missing-momentum region.
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 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 (Px/Pz)A(Px/Pz)H1 is 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.
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