Radiative corrections to elastic electron-carbon scattering cross sections in comparison with experiment

Abstract

The influence of dispersion on the differential scattering cross section in the vicinity of the first diffraction minimum is revisited for collision energies between 200 and 450 MeV. Transient nuclear excitations in the giant resonance region with angular momentum L \leq 3 are taken into consideration within updated numerics. Moreover, the deviations of the nonperturbative QED corrections from the conventionally used smooth Born predictions are accounted for. A qualitative agreement with the measurements is only obtained for the lowest energy, while dispersion within the present model is too small at the higher energies.

Figures (5)

• Figure 1: Angular distribution of the cross section change $\Delta \sigma^{\rm box}(L,\omega_L)$ by the transient excitation of a state with energy $\omega_L$ and angular momentum $L$ for 300.5 MeV electrons colliding with $^{12}$C. Shown are the results for the dipole states at 23.5 MeV $(-\cdot -\cdot -)$, at 17.7 MeV $(----)$ and for the quadruploe states at 4.439 MeV $(\cdots\cdots)$ and 9.84 MeV $(-\cdots -)$. Included is their sum $\Delta \sigma^{\rm box}$ (---------).
• Figure 2: Total cross section change $\Delta \sigma^{\rm theor}$ (------) from (\ref{['2.9']}) in 238.1 MeV $e + ^{12}$C collisions as function of the scattering angle $\vartheta_f$. Also shown is the result $\Delta \sigma^{\rm box}$ from dispersion $(-\cdot -\cdot -)$, as well as the difference $d(QED)=\Delta \sigma^{\rm QED} -\Delta \sigma^{\rm QED,B-C}\;(\cdots\cdots).$ The experimental points $(\bullet -- \bullet)$, denoting $\Delta \sigma^{\rm exp}$, are deduced from the data of Offermann et al. Of91.
• Figure 3: Total cross section change $\Delta \sigma^{\rm theor}$ (------) in 300.5 MeV $e + ^{12}$C collisions as function of the scattering angle $\vartheta_f$. Also shown is the result $\Delta \sigma^{\rm box}$ from dispersion $(-\cdot -\cdot -)$. The experimental points $(\bullet -- \bullet)$, denoting $\Delta \sigma^{\rm exp}$, are deduced from the data of Reuter et al. Re82.
• Figure 4: Total cross section change $\Delta \sigma^{\rm theor}$ (------) in 431.4 MeV $e + ^{12}$C collisions as function of the scattering angle $\vartheta_f$. Also shown is the result $\Delta \sigma^{\rm box}$ from dispersion $(-\cdot -\cdot -)$, as well as the QED difference $d(QED)\;(\cdots\cdots)$, using $\omega_0=0.0863$ MeV for the bremsstrahlung cutoff. The experimental points $(\bullet -- \bullet)$, denoting $\Delta \sigma^{\rm exp}$, are deduced from the data of Offermann et al. Of91.
• Figure 5: Angular distribution of the cross section change $\Delta \sigma^{\rm box}$ by dispersion for electrons colliding with $^{12}$C at energies 238.1 MeV $(-\cdot -\cdot -)$, 300.5 MeV (---------) and 431.4 MeV $(----)$.