Radiative corrections to the spin asymmetry in elastic polarized electron-nucleus collisions at high energy

TL;DR

The paper addresses radiative corrections to the beam-normal spin asymmetry $S$ in elastic $e$–nucleus scattering by combining dispersive two-photon exchange with nonperturbative QED corrections implemented as $V_{ m vac}$ and $V_{ m vs}$ in the Dirac equation. It extends dispersion calculations to GeV energies and evaluates the total effect $S_{ m tot}$ for $^{208}$Pb and $^{12}$C, finding that QED corrections can dominate in many cases, while dispersion remains significant at lower energies and larger angles for Pb. Across the studied kinematics, the theory largely fails to explain high-energy experimental measurements beyond 500 MeV, particularly for Pb, indicating unresolved physics (the Pb puzzle) at GeV energies. The work highlights the relative importance of dipole, quadrupole, and octupole nuclear excitations in shaping $S$ and demonstrates the necessity of combining dispersion with nonperturbative QED effects for accurate predictions in elastic polarized electron–nucleus collisions.

Abstract

Modifying the numerical codes, dispersion corrections to the beam-normal spin asymmetry which arise from low-lying transient nuclear excitations up to 30 MeV, are estimated for collision energies between 50 MeV and 1 GeV. A nonperturbative calculation of vacuum polarization and the vertex plus self-energy correction, using optimized potentials, indicates that for small scattering angles both these quantum electrodynamical (QED) effects on the spin asymmetry decrease with energy above 200 MeV and can be neglected at high energies. Examples are given for the 12C and 208Pb nuclei. The available measurements of the spin asymmetry at collision energies beyond 500 MeV cannot be explained by the present theory.

Figures (10)

• Figure 1: Feynman box diagram. The single line represents the electron with initial, intermediate and final momenta $k_i,\;p$ and $k_f$, respectively, and the double line represents the nucleus which is in an intermediate excited state $N^\ast$. The virtual photon momenta are denoted by $q_1$ and $q_2$.
• Figure 2: Sherman function $S_{\rm coul}$ (a) in $e+^{208}$Pb collisions at $\vartheta_f =5^\circ$ and $25^\circ$ as a function of collision energy $E_{\rm i,kin}=E_i-c^2$ and (b) in $e+^{208}$Pb and (c) in $e+^{12}$C collisions at 570 and 950 MeV as a function of scattering angle $\vartheta_f.$ Results from Gaussian charge distribution in (a) at $25^\circ$ (-------) and $5^\circ\; (-\cdot -\cdot -)$ and in (b) and (c) at 950 MeV (-------) and 570 MeV $(-\cdot -\cdot -)$. Results from Fourier-Bessel charge distribution in (a) at $25^\circ \;(----)$ and in (b) and (c) at 950 MeV $(----)$ and 570 MeV $(\cdots\cdots)$.
• Figure 3: Spatial dependence of the Uehling potential $V_{\rm vac}\;(-\cdot -\cdot -)$ and of the vertex plus self-energy potential $V_{\rm vs}\;(----)$ (a) for $^{208}$Pb and (b) for $^{12}$C. Included is the Coulombic potential $V_T$ (-------). For better visibility $V_{\rm vs}$ is multiplied by a factor of 10 and $V_{\rm vac}$ by a factor of 100.
• Figure 4: Large-distance behaviour of $V_{\rm vac}\;(-\cdot -\cdot -)$ and of $V_{\rm vs}\;(----)$ (a) for $^{208}$Pb and (b) for $^{12}$C. Also shown is $V_{\rm vs}^{\rm mod}$ with the fitted tail (--------).
• Figure 5: Relative change $dS$ of the spin asymmetry from 56 MeV $e + ^{208}$Pb collisions as a function of scattering angle $\vartheta_f$. In (a), the dispersive change $dS_{\rm box}$ is shown (-------), together with its contributions from all dipole states $(-\cdot -\cdot-)$, all quadrupole states $(----)$ and all octupole states $(\cdots\cdots)$. (b) shows the QED changes (---------), resulting from vacuum polarization $(-\cdot -\cdot -)$ and the vs correction $(----)$. Also shown is the dispersive change $dS_{\rm box}$ from (a) $(\cdots\cdots)$. The sum of all radiative changes is included $(\ast \ast \ast)$. (Updating Fig.8b in Jaku24.)