The experiment yields a capture rate $ R = \sigma_0 v / \pi b^3 = (1.0 \pm 0.2) \times 10^{15} $ sec$^{-1}$, assuming the radius $ b = 2.2 \times 10^{-11} $ cm and velocity $ v_0 = 8 \times 10^9 $ cm/sec. The capture rate is compared to the competing process $ p(\pi^{-}, \gamma)n $. Bernardini's analysis of cross sections for $ p(\gamma, \pi^{+})n $, $ d(\gamma, \pi^{+})2n $, and $ d(\gamma, \pi^{-})2p $ at 170-190 MeV suggests that the initial slope of $ \beta_s^0 - \alpha_s^0 $ is $ \pm(9.2^\circ)\eta' $, conflicting with the experiment's result of $ -(16.5^\circ)\eta' $. Bethe and Noyes explain this discrepancy by assuming the slope cannot be extrapolated to Panofsky's energy, and they fit the data with a smooth curve for $ \beta_2^0 - \alpha_2^0 $ versus $ \eta' $. This leads to a conclusion that $ \beta_2^0 $ changes sign between 20 and 30 MeV, suggesting a Jastrow potential for the phase shift. The paper discusses quantum electrodynamics (QED) at small distances, focusing on the renormalized propagation functions $ D_{FC} $ and $ S_{FC} $ for photons and electrons. These functions are investigated for momenta much greater than the electron mass, where the perturbation series terms have simple asymptotic forms. The series satisfy functional equations due to the renormalizability of QED. The function $ S_{FC} $ has an asymptotic form $ A[p^2/m^2][i\gamma \cdot p]^{-1} $, where $ A = A(e_1^2) $. The paper also explores the behavior of the charge distribution in the vacuum, showing that its shape at small distances depends on the coupling constant only through a scale factor. The propagation functions for large momenta relate to the magnitude of renormalization constants, and the unrenormalized coupling constant $ e_1^2 / 4\pi\hbar c $ may be infinite or finite. The paper concludes that the shape of the charge distribution is independent of the coupling constant at small distances, and the behavior of the propagation functions is connected to the renormalization constants. The results suggest that the effective charge distribution has a $ \delta $-function form at high momenta, with the bare charge being finite or infinite depending on the coupling constant. The paper alsoThe experiment yields a capture rate $ R = \sigma_0 v / \pi b^3 = (1.0 \pm 0.2) \times 10^{15} $ sec$^{-1}$, assuming the radius $ b = 2.2 \times 10^{-11} $ cm and velocity $ v_0 = 8 \times 10^9 $ cm/sec. The capture rate is compared to the competing process $ p(\pi^{-}, \gamma)n $. Bernardini's analysis of cross sections for $ p(\gamma, \pi^{+})n $, $ d(\gamma, \pi^{+})2n $, and $ d(\gamma, \pi^{-})2p $ at 170-190 MeV suggests that the initial slope of $ \beta_s^0 - \alpha_s^0 $ is $ \pm(9.2^\circ)\eta' $, conflicting with the experiment's result of $ -(16.5^\circ)\eta' $. Bethe and Noyes explain this discrepancy by assuming the slope cannot be extrapolated to Panofsky's energy, and they fit the data with a smooth curve for $ \beta_2^0 - \alpha_2^0 $ versus $ \eta' $. This leads to a conclusion that $ \beta_2^0 $ changes sign between 20 and 30 MeV, suggesting a Jastrow potential for the phase shift. The paper discusses quantum electrodynamics (QED) at small distances, focusing on the renormalized propagation functions $ D_{FC} $ and $ S_{FC} $ for photons and electrons. These functions are investigated for momenta much greater than the electron mass, where the perturbation series terms have simple asymptotic forms. The series satisfy functional equations due to the renormalizability of QED. The function $ S_{FC} $ has an asymptotic form $ A[p^2/m^2][i\gamma \cdot p]^{-1} $, where $ A = A(e_1^2) $. The paper also explores the behavior of the charge distribution in the vacuum, showing that its shape at small distances depends on the coupling constant only through a scale factor. The propagation functions for large momenta relate to the magnitude of renormalization constants, and the unrenormalized coupling constant $ e_1^2 / 4\pi\hbar c $ may be infinite or finite. The paper concludes that the shape of the charge distribution is independent of the coupling constant at small distances, and the behavior of the propagation functions is connected to the renormalization constants. The results suggest that the effective charge distribution has a $ \delta $-function form at high momenta, with the bare charge being finite or infinite depending on the coupling constant. The paper also