Radiative energy losses are very important in regulating the cosmic ray electron and/or positron (CRE) spectrum during their propagation in the Milky Way. Particularly, the Klein–Nishina (KN) effect of the inverse Compton scattering (ICS) results in less efficient energy losses of high-energy electrons, which is expected to leave imprints on the propagated electron spectrum. It has been proposed that the hardening of CRE spectra around 50 GeV observed by Fermi-LAT, AMS-02, and DAMPE could be due to the KN effect. We show in this work that the transition from the Thomson regime to the KN regime of the ICS is actually quite smooth compared with the approximate treatment adopted in some previous works. As a result, the observed spectral hardening of CREs cannot be explained by the KN effect. It means that an additional hardening of the primary electrons spectrum is needed. We also provide a parameterized form for the accurate calculation of the ICS energy-loss rate in a wide energy range.

辐射能量损失对于调节宇宙射线电子和/或正电子 (CRE) 在银河系中传播的光谱非常重要。特别是，逆康普顿散射 (ICS) 的 Klein-Nishina (KN) 效应导致高能电子的能量损失效率较低，预计这会在传播的电子光谱上留下印记。有人提出，Fermi-LAT、AMS-02 和 DAMPE 观察到的 CRE 光谱在 50 GeV 附近的硬化可能是由于 KN 效应。我们在这项工作中表明，与以前的一些工作中采用的近似处理相比，ICS 从 Thomson 机制到 KN 机制的过渡实际上是相当平滑的。因此，观察到的 CRE 的光谱硬化不能用 KN 效应来解释。这意味着需要对初级电子光谱进行额外的硬化。我们还提供了一种参数化形式，用于精确计算宽能量范围内的 ICS 能量损失率。