In this paper, we report our calculations of the triple-differential cross section (TDCS) for the relativistic $(e,2e)$ process with a twisted electron beam on Cu and Ag atomic targets in coplanar asymmetric geometry mode. The theoretical formalism has been developed in the first Born approximation, in which we use the Dirac plane wave as well as the twisted electron wave for the incident electron beam to study the effect of various parameters of the twisted electron beam on the $(e,2e)$ process. We use a Dirac plane-wave function, semirelativistic Coulomb wave function, and Darwin wave function for the scattered, ejected, and K-shell electron, respectively. We compare the angular profiles of the TDCS of the twisted electron impact $(e,2e)$ process with that of the plane wave. We segregate the TDCS for charge-charge interaction and current-current interaction with their interference term and study the effect of different parameters of the twisted electron beam on them. The study is also extended to the macroscopic Cu and Ag targets to further investigate the effect of the opening angle of the twisted electron beam on TDCS. The spin asymmetry in TDCS caused by the polarized incident electron beam is also studied to elucidate the effects of the twisted electron beam on the $(e,2e)$ process.

中文翻译：

---

使用扭曲电子束对 Cu 和 Ag 进行半相对论 (e,2e) 研究

在本文中，我们报告了我们对相对论的三微分截面 (TDCS) 的计算 $(\mathrm{电子},2\mathrm{电子})$以共面非对称几何模式在 Cu 和 Ag 原子靶上使用扭曲电子束进行处理。理论形式是在第一个波恩近似中发展起来的，其中我们使用狄拉克平面波以及对入射电子束的扭曲电子波来研究扭曲电子束的各种参数对入射电子束的影响。$(\mathrm{电子},2\mathrm{电子})$过程。我们分别对散射、喷射和K层电子使用狄拉克平面波函数、半相对论库仑波函数和达尔文波函数。我们比较了扭曲电子撞击的 TDCS 的角度分布$(\mathrm{电子},2\mathrm{电子})$与平面波的过程。我们将电荷-电荷相互作用和电流-电流相互作用的 TDCS 与其干涉项分开，并研究扭曲电子束的不同参数对它们的影响。该研究还扩展到宏观 Cu 和 Ag 目标，以进一步研究扭曲电子束的张角对 TDCS 的影响。还研究了由偏振入射电子束引起的 TDCS 中的自旋不对称性，以阐明扭曲电子束对$(\mathrm{电子},2\mathrm{电子})$ 过程。