The paper by Bethe and Heitler discusses the stopping power of matter for fast particles, focusing on three processes: ionization, nuclear scattering, and radiation emission. The authors provide a detailed analysis of the third process, which involves the emission of radiation under the influence of the electric field of a nucleus. They derive the differential cross-section for energy loss by radiation and consider the effect of screening on this process. The results are compared with experimental data, particularly for very high energies (>137mc²), where discrepancies are noted. Additionally, the paper explores the "twin birth" process, where a positive and negative electron are created from a light quantum in the presence of a nucleus. This process is shown to be consistent with recent measurements for γ-rays of 3–10mc². The authors also derive the probability of this process and compare it with earlier estimates. The authors further discuss the radiation probability as a function of the impact parameter, showing that the probability is roughly proportional to 1/r³ for small distances from the nucleus and decreases more rapidly for larger distances. They compare their results with classical electrodynamics and find that their quantum mechanical treatment yields a smaller radiation probability. Finally, the paper examines the energy loss of fast electrons by radiation and collisions, providing numerical results for various materials. It highlights that the energy loss by radiation is much greater than that by inelastic collisions for high energies, and the range of fast electrons is determined by the balance between radiation and collision energy loss. The authors also discuss the straggling effect, where the actual energy loss may differ significantly from the average, leading to variations in the electron's range.The paper by Bethe and Heitler discusses the stopping power of matter for fast particles, focusing on three processes: ionization, nuclear scattering, and radiation emission. The authors provide a detailed analysis of the third process, which involves the emission of radiation under the influence of the electric field of a nucleus. They derive the differential cross-section for energy loss by radiation and consider the effect of screening on this process. The results are compared with experimental data, particularly for very high energies (>137mc²), where discrepancies are noted. Additionally, the paper explores the "twin birth" process, where a positive and negative electron are created from a light quantum in the presence of a nucleus. This process is shown to be consistent with recent measurements for γ-rays of 3–10mc². The authors also derive the probability of this process and compare it with earlier estimates. The authors further discuss the radiation probability as a function of the impact parameter, showing that the probability is roughly proportional to 1/r³ for small distances from the nucleus and decreases more rapidly for larger distances. They compare their results with classical electrodynamics and find that their quantum mechanical treatment yields a smaller radiation probability. Finally, the paper examines the energy loss of fast electrons by radiation and collisions, providing numerical results for various materials. It highlights that the energy loss by radiation is much greater than that by inelastic collisions for high energies, and the range of fast electrons is determined by the balance between radiation and collision energy loss. The authors also discuss the straggling effect, where the actual energy loss may differ significantly from the average, leading to variations in the electron's range.